April 13, 2024

Arithmetic – Mathematics – Paper VI – WBCS Main Question Paper

By Sutirtha Datta WBCS Mains Question Paper 0 Comments

Contents

WBCS Main Math paper

Video explanations are given at the end of every year questions.

WBCS Main Question Paper – 2022

The average of 5 consecutive numbers is 15. The greatest number is

(A) 17

(B) 19

(D) 15

Find the value of x from the following equation.

(A) 9

(B) 18

(D) 4

The hundreds digit of the square root of the square number 3,15,844 is

(A) 3

(B) 4

(C) 5

(D) 6

Value of

(A) 7²³ × 5

(B) 7²³ × 175

(C) 7²² × 175

(D) 7²³ × 35

is equal to

(A) 2

(B) 3

(C) 4

(D) 6

Which of the following numbers is divisible by 3, 4, 5 and 7?

(A) 3150

(B) 1400

(C) 2940

(D) 3570

A loan was repaid in two annual instalments of ₹ 3,630 each. If the rate of interest be 10% per annum compounded annually, then find the sum that was borrowed.

(A) ₹ 5,200

(B) ₹ 6,100

(C) ₹ 6,300

(D) ₹ 5,600

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In a seminar the number of participants in Mathematics, Physics and Biology are 192, 240 and 168 respectively. Find the minimum number of rooms required if in each room same number of participants is to be seated and all of them being of the same subject.

(A) 20

(B) 25

(D) 30

The smallest number which is being divided by 8, 9, 12 and 15 always leaves 1 as a remainder is

(A) 361

(B) 359

(D) 197

The speed of a bus is 54 km/h excluding stoppages and 45 km/h including stoppages. The bus will stop per hour for

(A) 8 minutes

(B) 10 minutes

(D) 15 minutes

A person has deposited some amount in a bank and becomes ₹500 in 3 years and ₹540 in 5 years. The rate of interest is

(A) 4%

(B) 4⁶⁄₁₁%

(D) 5%

In two types of brass, the ratio of copper and zinc are 8 : 3 and 15 : 7 respectively. If these two types of brasses are mixed in the ratio 5 : 2, then in the mixture the ratio of copper and zinc will be

(A) 5 : 2

(B) 2 : 5

(D) 3 : 5

then which of the following relations is true?

(A) x < y < z

(B) z < x < y

(D) x > y >z

A keeps 10 ships for 3 weeks and B keeps 15 ships for 4 weeks. Find the ratio of the rent paid by them.

(A) 1 : 2

(B) 2 : 1

(D) 1 : 3

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To cover a distance a man first goes ⅜ of the journey by train, 20% of the remaining by bus and still he has 6 km. The total distance is

(A) 8 km

(B) 10 km

(C) 12 km

(D) 16 km

A batsman has certain average of runs for 11 innings. In the 12th innings he makes a score of 90 runs, thereby increasing his average by 5. His average after the 12th innings is

(A) 30

(B) 35

(D) 32

The annual increase in the population of a town be 10% and the present population is 13310. The population last two years ago was

(A) 10000

(B) 11000

(D) 11500

A hotel bill for a number of people for overnight is ₹4,800. If there were 4 more people, the bill each person had to pay, would have reduced by ₹200. Then the number of people staying overnight is

(A) 8

(B) 6

(D) 12

Find the equation of a line parallel to y-axis and passing through the point (-3,4).

(A) x + 3 = 0

(B) x – 3 = 0

(D) x – 4 = 0

When 50% of one number is added to a second number, the second number increases to its four-third. What is the ratio between the first number and the second number?

(A) 3 : 2

(B) 3 : 4

(C) 2 : 3

(D) 1 : 3

Equal weights of alloys ‘x’ and ‘y’ which contain zinc and tin in the proportion of 8 : 3 and 6 : 5 respectively are melted to form a third alloy ‘z’, ‘z’ contains zinc and tin in the proportion of

(A) 4 : 7

(B) 3 : 5

(D) 7 : 4

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A person was appointed for a 50 day’s job on a condition that he will fined ₹6 for everyday he remains absent. After completion of the work, he got ₹420. How many days he did not work?

(A) 15 days

(B) 5 days

(C) 10 days

(D) 20 days

Find the number which is subtracted from the numbers in the ratio 11 : 23 so that the ratio becomes 1 : 3.

(A) 5

(B) 6

(D) 8

A motorboat covers a certain distance downstream in a river in five hours. It covers the same distance upstream in six hours. The speed of water is 2 km/h. Then the speed of the boat in still water is

(A) 20 km/h

(B) 22 km/h

(D) 25 km/h

Three friends started a partnership business with capitals ₹5,000, ₹6,000 and ₹7,000 respectively. After one year they found a loss of ₹1,800. To keep the capital same they decided to share the loss among themselves in the ratio of their capitals. The amount each one has to pay is

(A) ₹490, ₹610, ₹700

(B) ₹490, ₹600, ₹710

(D) ₹500, ₹600, ₹700

A mixture of 40 L of alcohol and water contains 40% water. How much water should be added to the mixture so that new mixture so that new mixture contains 20% water?

(Canceled By PSC)

(A) 5 L

(B) 9 L

(D) 6 L

A computer depreciates at a rate of 25% p.a. If it was worth ₹26,000 new, how many full years must pass, before it worth less than half of its original value?

(A) 2 years

(B) 3 years

(D) 1 year

If the value of a gold coin is increased by 20% each year, then the average percentage increase of the gold coin over three years is

(A) 80.5%

(B) 60%

(C) 72.8%

(D) 70.1%

At a certain school, there are 320 juniors and 180 seniors. The average absenteeism rate is 6¼% for juniors and 8⅓% for seniors. Then the average absenteeism rate overall for the school is

(A) 5%

(B) 6%

(C) 7%

(D) 8%

A began a business with ₹10,500 and is joined afterwards by B with ₹18,000. After how many months did B join, if the profit at the end of the year is divided equally?

(A) 15 months

(B) 10 months

(C) 5 months

(D) Couldn’t be determined

The smallest number by which 6400 must be multiplied to make a perfect cube is

(A) 2

(B) 4

(D) 10

The ratio in which two sugar solution of the concentrations 15% and 40% are to be mixed to get a solution of concentration 30% is

(A) 2 : 3

(B) 3 : 2

(D) 9 : 8

Which of the following numbers has the maximum number of divisors?

(A) 108

(B) 99

(D) 44

A boy was asked to find 3½% of a sum of money. He misread the question and found 5½% of it. His answer was ₹247.50. The correct answer is

(A) ₹100

(B) ₹157.50

(D) ₹160

At a fair, a boy tries his skill in shooting. He was to receive ₹2 for hitting the ‘bulls eye’ and had to pay ₹1 for missing it. He tried 60 shots but received only ₹12. Then he hit the bull’s eye

(A) 12 times

(B) 6 times

(C) 24 times

(D) 30 times

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The population of a town is 24000. If the number of males is increased by 6% and the number of females by 9%, then there would be 25620. The number of males and females in the town are

(A) 18000, 6000

(B) 16000, 8000

(D) 17000, 7000

In 4 years ₹6,000 amounts to ₹8,000. In what time at the same rate of interest will ₹525 amounts to ₹700?

(A) 4 years

(B) 3 years

(D) 5 years

A peon has a salary of ₹1,000 per month and a carpenter earns ₹30 per day, but he is idle for 65 days in the year. The ratio of their income is

(A) 4 : 5

(B) 5 : 6

(C) 4 : 3

(D) 3 : 4

The ratio of ladies and gentlemen at a party was 3 : 2. When 20 more gentlemen joined the party, the ratio was reversed. The number of ladies present at the party was

(A) 18

(B) 36

(C) 24

(D) 30

A tea seller faces 20% loss selling a certain brand of tea at the rate of ₹80 per kg. By selling another brand of tea at the rate of ₹200 per kg, he makes a profit of 25%. In what ratio the seller needs to make a profit by selling the mixed branded tea at the rate of ₹150 per kg?

(A) 1 : 2

(B) 2 : 3

(C) 2 : 1

(D) 3 : 2

The area of a circle is increased by 22 sq. m. when its radius is increased by 1 m. Find the original radius of the circle.

(A) 6 m

(B) 3 m

(D) 3⅕ m

The average temperature of a city in the first four days of a month was 58 degree. The average of the 2nd, 3rd, 4th and 5th days was 60 degree. If the temperatures of 1st and 5th days were in the ratio 7 : 8, then what is the temperature of 5th day?

(A) 64 degree

(B) 62 degree

(D) None of the above

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The sum of two numbers is 150 and their H.C.F. is 15. The number of possible pairs is

(A) 2

(B) 3

(D) 5

63.

is equal to

(A) ¹⁰⁰¹⁄₉₉₉

(B) ⁹⁹⁹⁄₁₀₀₁

(C) ¹⁰⁰¹⁄₃

(D) ⁵⁄₁₀₀₁

A bus maintains an average speed of 60 km/h while going from P to Q and maintains an average speed of 90 km/h while coming back. The average speed of bus is

(A) 75 km/h

(B) 72 km/h

(D) 80 km/h

A person has money to buy 42 suitcases at the rate of ₹500 each. If the cost per suitcase is increased by ₹100, then number of suitcases he can buy now is

(A) 30

(B) 35

(D) 40

Mohit purchased a plot of land for ₹12,500. After 1 year due to recession the value of his land fell by 5%. In the 2nd year, the value increased by 8%. Then the value of the land after 2 years is

(A) ₹12,500

(B) ₹12,000

(D) ₹12,825

A sum of money is borrowed and paid back in two annual installments of ₹1,764 each allowing 5% compound interest. What was the sum borrowed?

(A) ₹4,000

(B) ₹3,340

(D) ₹3,280

A man sold 2 articles at the same price ₹2,970 each. On one he made a loss of 10% and on the other a gain of 10%. The overall gain or loss percentage is

(A) loss 1%

(B) gain 1%

(D) gain 0.1%

A business man marks his good at 20% above the cost price. He allows the customer a discount of 8% on market price. His net percentage of profit is

(A) 10.4%

(B) 10%

(D) 10.6%

The radius of a wheel is 14 m. How many revolution will it make in travelling 880 m?

(A) 10

(B) 12

(D) 16

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The numerator of a fraction is 6 less than its denominator. If 3 is added to the numerator, the fraction becomes equal to ⅔. Then the original fraction is

(A) ⁷⁄₁₃

(B) ¹⁄₇

(C) ³⁄₉

(D) ⁵⁄₁₁

If 6 men can harvest a field in 60 working hours and a man works three times as fast as a boy. Then 10 boys can harvest a field in

(A) 60 hours

(B) 40 hours

(D) 108 hours

(A) 18.6

(B) 1860

(D) 1.86

Divide ₹2,600 in 3 parts in such a way that the interest at 4% of the first part, 6% of the 2nd part and 8% of the 3rd part becomes equal.

(A) ₹1200, ₹800, ₹600

(B) ₹1100, ₹900, ₹600

(D) ₹1200, ₹1000, ₹800

In a restaurant, John has 4 choices for starters, 6 choices for the main course and 5 choices for dessert. Then number of different 3 course meals John can order is

(A) 100

(B) 150

(C) 120

(D) 200

A block of cheese 5 cm by 6 cm by 8 cm is covered with wax. If the cheese is cut into one centimetre cubes, then number of cubes not having wax on them is

(A) 72

(B) 240

(D) 120

Successive discounts of 10% and 30% are equivalent to a single discount of

(A) 73%

(B) 36%

(D) 37%

A certain amount of money is kept for 2 years at certain simple interest. If the interest rate is 3% higher, then it will bring ₹300 more. The amount of money is

(A) ₹2,000

(B) ₹2,500

(D) ₹5,000

In a partnership between A and B, A’s capital is ⅖th of the total and invested for ⅔rd year. If his share of profit is ⁴⁄₇ of the total, then how long is B’s capital in the business?

(A) 6 months

(B) 4 months

(D) 3 months

Then the value of x is

(A) 1

(B) 2

(D) 4

The average of 7 consecutive number is 20. The largest of these numbers is

(A) 24

(B) 23

(D) 20

At the time of wedding the bride’s age was ¾ of the groom’s age. After 8 years her age is ⅘ of her husband’s age. Then the age of the bride at the time of her wedding is

(A) 24 years

(B) 18 years

(D) 26 years

In a partnership business, Amal invested capital double the capital of Palash. The ratio of the period of investment is ½ : ⅓. Then the ratio of their profit is

(A) 1 : 3

(B) 3 : 1

(D) 2 : 3

A takes as much time to do a piece of work as B and C take to do it working together. If A and B together can do the same work in 10 days and C alone can do it in 20 days, find the time in which B will finish this work.

(A) 40 days

(B) 60 days

(D) 20 days

Two cyclists start from the same place in opposite direction and goes towards north at 18 km/h and the other goes towards south at 20 km/h. What time will they need to apart 47.5 km?

(A) 2 hours

(B) 1¼ hours

(D) 2½ hours

The value of

(A) 52

(B) 53

(D) 56

If (2a+1)(2a+2)(2a+3)(2a+4)+q is a perfect square, then q = ?

(A) 24

(B) 1

(D) -8

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Vandana bought a watch for ₹600 and sold it on the same day for ₹688.50 at a credit of 9 months and this way she gained 2%. Find the rate of interest per annum.

(A) 16⅔ %

(B) 15⅔ %

(D) 5⅔ %

A student was asked to multiply a number by ³⁄₂ but he divided the number by ³⁄₂. His result was therefore 10 less than the correct answer. Find the number.

(A) 10

(B) 12

(D) 20

The G.C.M. of two numbers is 17 and their product is 6936. The no. of pairs of such numbers is

(A) 4

(B) 2

(D) 5

A and B start from the same place and travel in the same direction, B starting 2 hours after A. If A travels 40 km/h and B travels at 50 km/h, then the distance the have travelled when B overtakes A is

(A) 400 km

(B) 500 km

(D) 550 km

The 8% simple interest on a certain amount of money for 3 years is half the 10% compound interest on ₹8,000 for 2 years. The amount on which simple interest is calculated

(A) ₹3,500

(B) ₹3,600

(D) ₹4,000

The angles of a triangle are in arithmetic progression. If one of the angles is 75°, then the other two angles are

(A) 65°, 85°

(B) 60°, 90°

(C) 45°, 60°

(D) 55°, 65°

If 69.5 is the mean of 72, 70, x, 62, 50, 71, 90, 64, 58 and 82, then the value of x is

(A) 75

(B) 67

(D) 76

A 2-digit number is such that the unit’s digit is four times the ten’s digit and if 54 is added to the number, the digits are reversed. Then the number is

(A) 14

(B) 28

(D) 41

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A can with 30 marbles weighed 120 gm. The same can with 15 marbles weighed 95 gm. Then the weight of the can is

(A) 50 gm

(B) 60 gm

(C) 70 gm

(D) 80 gm

40 men complete ⅓rd of a work in 40 days. How many more men should be employed to finish the rest of the work in 50 more days?

(A) 12

(B) 20

(D) 24

A train leaves place A at 5 am and reaches place B at 9 am. Another train leaves place B at 7 am and reaches place A at 10:30 am. At what time do they cross each other?

(A) 6:56 am

(B) 7:56 am

(D) 8:30 am

The sum of two numbers is 1400. If the larger number is decreased by 20% and the smaller number is increased by 20%, then the resulting numbers are equal. The two numbers are

(A) 740, 660

(B) 840, 560

(D) 820, 580

The monthly salaries of A and B are in the ratio 3 : 5. Each receives an increment of ₹500. If the ratio of their salaries now stands at 7 : 11, then the salary of A, before increment was

(A) ₹2,500

(B) ₹3,000

(D) ₹4,000

Train A crosses a pole in 25 seconds and train B does the same in 1 minute 15 seconds. Length of train A is half the length of train B. What is the ratio between the speed of A and B?

(A) 3 : 4

(B) 4 : 3

(C) 3 : 2

(D) 2 : 3

The product of the digits of a two-digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2, then the number is

(A) 64

(B) 46

(C) 38

(D) 83

A shopkeeper buys a number of books for ₹80. If he had bought 4 more books for the same amount, each book would have cost ₹1 less. How many books did he buy?

(A) 16

(B) 20

(D) 22

The difference between compound interest and simple interest for 2 years on ₹22,500 at 6% p.a. is

(A) ₹225

(B) ₹181

(C) ₹81

(D) ₹220

The sum of first 102 positive integers is

(A) 5250

(B) 5251

(D) 5253

If the number 472573* is completely divisible by 72, then which number should replace the star?

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(A) 4

(B) 5

(D) 7

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If the difference between 62% and 80% of a number is 198, then the difference between 92% and 56% of the number will be

(A) 396

(B) 3564

(D) 360

If the first and the third terms of a G.P. are 2 and 8 respectively, then its second term is

(A) -4

(B) ±4

(D) 0

In a multiple choice exam of 30 questions, a correct answer earns 2 marks, an incorrect answer loses 3 marks and an unanswered question scores 0 marks. If Raj left out 6 questions and his score was 28, then number of questions he gets correct is

(A) 22

(B) 20

(D) 15

Two men undertake to do a piece of work for ₹200. One alone can do it in 6 days, the other in 8 days. With the help of a boy they finish it in 3 days. How much is the share of the boy?

(A) ₹20

(B) ₹25

(D) ₹40

5% of a = b, then b% of 20 is same as

(A) 20% of ᵃ⁄₂

(B) 50% of ᵃ⁄₂₀

(D) 20% of ᵃ⁄₂₀

Amal can do a piece of work in 12 days. Mihir is found to be 50% more efficient than Amal. If Mihir is given the piece of work, then he will complete it by

(A) 6 days

(B) 8 days

(D) 10 days

After spending 88% of his money, a boy found he still had ₹372 left. Initially he had

(A) ₹3,372

(B) ₹4,400

(D) ₹3,100

How much water must be added to 5 litres of a 90% acid solution to make a 75% acid solution?

(A) 5.5 litres

(B) 0.5 litre

(C) 1 litre

(D) 4.5 litres

Divide ₹2,602 between X and Y, so that the amount of X after 7 years is equal to the amount of Y after 9 years, the interest being compounded at 4% per annum.

(A) ₹1352, ₹1250

(B) ₹1250, ₹1352

(D) ₹1400, ₹1202

A loan amount ₹11,000 is to be paid in two equal annual installments. If the rate of interest be 20% compounded annually, then the value of each installment is

(A) ₹7,200

(B) ₹7,100

(D) ₹7,500

If a glass holds 275 ml, how many of these glasses can be filled from a 2-liter drink of lemonade?

(A) 8 full glasses

(B) 7 full glasses

(D) 6 full glasses

The average of 8 numbers is 6 and the average of 6 other numbers is 8. What is the average of all 14 numbers?

(A) 6

(B) 6⁶⁄₇

(D) 7⁵⁄₇

Capacity of tap B is 80% more than that of A. If both the taps are opened simultaneously, they take 45 hours to fill the tank. How long will B take to fill the tank alone?

(A) 72 hours

(B) 48 hours

(D) 70 hours

In an examination, it is required to get 40% marks to qualify. A candidate secured 150 marks and failed by 10 marks. What are the maximum marks of the examination?

(A) 500

(B) 400

(D) 350

A person gets ₹3,700 per week plus 2% commission on the sale of goods in excess of ₹10,000. If his a-week sales total is ₹24,000, then the week’s wages earned by the person is

(Canceled By PSC)

(A) ₹3,840

(B) ₹4,980

(D) ₹4,280

Hospital is 12 km towards east of Rupin’s house. His school is 5 km towards south of Hospital. What is the shortest distance between Rupin’s house and school?

(A) 16 km

(B) 17 km

(D) 13 km

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A person was driving a car in fog. He passed a pedestrian who was walking at the speed of 2 km/h in the same direction. The pedestrian could see the car for 6 minutes and up to a distance of 0.6 km. What was the speed of the car?

(A) 8 km/h

(B) 10 km/h

(D) 12 km/h

The capacities of two glasses are same. They are filled with ⅔ part and ⅖th part of water respectively. Remaining part of both the glasses are filled with milk. If mixtures of both the glasses are mixed in a big glass, what is the ratio of water and milk in it?

(A) 8 : 7

(B) 5 : 7

(D) 9 : 2

A dealer sold an article at a loss of 10%. If he had sold for ₹125 more, he would have gained 15%. The cost price of the article is

(A) ₹300

(B) ₹500

(D) ₹1200

A survey in a city showed that the probability that a person smokes is ²⁄₉. If 40 people in a certain sample smoke, then number of people in the sample is

(A) 180

(B) 200

(D) 120

A runs 1⅔ times as fast as B. If A gives B a start of 40 m, how far must the winning post be so that A and B might reach it at the same time?

(A) 75 m

(B) 200 m

(C) 100 m

(D) 125 m

A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it has to increase its speed by 250 km/h from its usual speed. Then its usual speed is

(A) 1000 km/h

(B) 2500 km/h

(C) 750 km/h

(D) 800 km/h

Average age of A, B and C is 36 years. If average age of B and C is 30 years and age of B is 22 years, then what is the sum of the ages of A and C?

(A) 68 years

(B) 86 years

(D) 61 years

Cost of coffee A and B are ₹64 and ₹80 per 100 gm respectively. A blend of two is sold ₹86 per 100 gm. If a profit of 25% is to be earned on this blend, what should be the proportion of A and B in its composition?

(A) 8 : 5

(B) 9 : 2

(C) 7 : 3

(D) 3 : 2

A merchant has 100 kg of sugar. He sells a part of which at 9% profit and the rest at 9% loss. He gains 5% on the whole. The quantity sold at 9% loss is

(A) 18 kg

(B) 20 kg

(C) 22.23 kg

(D) 25 kg

A rectangular lawn 80 m × 60 m has two roads each 10 m wide running in the middle of it. One parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at ₹20 per sq. m.

(A) ₹35,000

(B) ₹39,000

(C) ₹26,000

(D) ₹41,000

The difference between the greatest and least numbers formed out of the digits 8, 9, 0, 7 is

(A) 9081

(B) 1809

(D) 2781

A certain sum of money amounts to ₹756 in 2 years and to ₹873 in 3 and half years at a certain rate of simple interest. The rate of interest p.a. is

(A) 10%

(B) 11%

(D) 13%

X is 20% heavier than Y and Z is 20% lighter than Y. The weight of Z is equal to

(A) ⅘ of X

(B) ⅗ of X

(D) ⅔ of X

The cost price and the selling price of a bag are in the ratio 4 : 5. The profit is

(A) 20%

(B) 25%

(D) 35%

If one-third of one-fourth of a number is 20, then one-tenth of that number is

(A) 24

(B) 36

(D) 54

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A company with 1000 shares of nominal value ₹150 declares an annual dividend of 10%. Then the total amount of dividend paid by the company is

(A) ₹15,000

(B) ₹10,000

(D) ₹1,500

In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and denominator both, the fraction reduces by ¹⁄₁₄. Then the fraction is

(A) ⁴⁄₇

(B) ⁸⁄₁₄

(D) ³⁄₁₄

A point P divides the line joining the points (2, 1) and (5, -8) in ratio 1 : 2. Also, the point P lies on the line 2x-y+k=0. Find the value of k.

(A) 6

(B) -8

(D) 8

The population of a town increases 5% annually, if its present population is 74970, what it was two years ago?

(A) 64200

(B) 68000

(D) 72000

In a State, each year the number of road accidents is decreased by 5% from the previous year due to road safety campaigns. The number of road accidents in the current year is 2916. 3 years ago this number was

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(A) 4000

(B) 5100

(D) 5000

Due to 25% fall in price of eggs, one can buy 2 dozen eggs more than before by investing ₹200. What was original price per dozen?

(A) ₹²⁰⁰⁄₆

(B) ₹³⁰⁰⁄₇

(D) ₹⁷⁰⁰⁄₅

The difference between the squares of two consecutive numbers is 65. The greatest number is

(A) 33

(B) 34

(D) 36

By selling an article for ₹31 a shopkeeper loses 7%. If he sells the article for ₹35, then what is gain or loss per cent?

(A) Loss 3%

(B) Gain 5%

(D) Gain 3%

What sum of money will amount to ₹520 in 5 years and to ₹568 in 7 years at simple interest?

(A) ₹400

(B) ₹120

(D) ₹220

181.

(A) 0

(B) 5

(D) 1

The value of

(A) ⅓

(B) ²⁄₉

(D) ⅔

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In what time will simple interest be ⅖ of the principal at 8% p.a.?

(A) 8 years

(B) 7 years

(C) 5 years

(D) 6 years

A man walking with ¾ of his usual speed, reaches office 20 minutes late. His usual time is

(A) 50 minutes

(B) 80 minutes

(D) 60 minutes

A man rows a boat 18 km in 4 hours downstream and returns upstream in 12 hours. The speed of the stream (in km/h) is

(A) 1

(B) 1.5

(D) 1.75

If a man sells two horses for ₹9,900 each, gaining 10% on one and losing 10% on the other. His loss is

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(A) ₹2

(B) ₹1

(D) ₹8

The difference between compound interest and simple interest on a sum for 2 years at 8% p.a. is ₹768. Find the sum.

(A) ₹1,10,000

(B) ₹1,20,000

(D) ₹1,70,000

If the ratio between 8 and 11 is the same as the ratio of (2x-y) to (x+2y), find the value of 7x/9y.

(A) ⁷⁄₉

(B) ³⁄₂

(D) ⁷⁄₂

Railway fares are increased by 50%. To return to the original rates they must be reduced by

(A) 33 %

(B) 33½ %

(C) 33⅓ %

(D) 33¼ %

If a = 25% of b = 10% of c, then a : b : c = ?

(A) 2 : 5 : 6

(B) 2 : 5 : 7

(D) 1 : 4 : 10

Aarti, Vinita and Kamala became partners in a business by investing money in the ratio 5 : 7 : 6. Next year, they increased their investment by 26%, 20% and 15% respectively. In what ratio profit earned during 2nd year should be distributed?

(A) 21 : 28 : 23

(B) 23 : 28 : 21

(D) 21 : 23 : 28

Rima has ₹1000 in denominations of ₹5 and ₹2 coins. If the number of two-rupee coins Rima has is five-eighths of the number of five-rupee coins, then five-rupee coins Rima has

(A) 100

(B) 120

(C) 160

(D) 200

A sum of ₹7,000 is divided among A, B and C in such a way that the shares of A and B are in ratio 2 : 3 and that of B and C are in the ratio 4 : 5. Then the share of C is

(A) ₹2,600

(B) ₹2,800

(C) ₹3,000

(D) ₹3,900

If the market price of a commodity is 32% more than its cost price and if 16% discount is given, then profit percentage is

(A) profit 9

(B) profit 10

(C) profit 10.88

(D) profit 11

If the cost price of 57 articles is equal to the selling price of 38 articles, then percentage profit is

(A) 20%

(B) 30%

(C) 50%

(D) 55%

Find the value of

(B)

When ⁵⁄₇ is expressed in decimal form, the digit in the 19th decimal place is

(A) 5

(B) 8

(C) 7

(D) 1

The ratio of investments of two partners is 11 : 12 and the ratio of their profits is 2 : 3. If A invests the money for 8 months, find for how much time B invests his money?

(A) 11 months

(B) 8 months

(D) 6 months

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WBCS Main Question Paper – 2021

The compound interest on Rs.2,000 in 2 years, if the rate of interest is 4% per annum for the first year and 3% per annum for the second year, will be

(A) Rs.143.40

(B) Rs.141.40

(D) Rs.142.40

The difference between the squares of two consecutive even integers is always divisible by

(A) 3

(B) 4

(D) 7

Two automobiles are 150 kilometers apart and traveling towards each other. One automobile is moving at 60 km/h and the other is moving at 40 km/h. In how many hours will they meet?

(A) 2.5

(B) 2.0

(D) 1.5

Sushant spent 18% of his monthly salary on buying electronic goods and 32% of the monthly salary on repair work in his house. Out of remaining amount he invested 42% in fixed deposit. If he was left with Rs. 12,325, how much is his annual salary?

(A) Rs. 5,18,000

(B) Rs. 5,15,600

(C) Rs. 5,10,000

(D) Rs. 5,01,000

The compound interest on Rs.30,000 at 7% per annum is Rs.4,347. The period (in years) is

(A) 2

(B) 2.5

(D) 4

The ratio of cost price to sale price is 20:23. What is the profit percentage?

(A) 20%

(B) 15%

(D) 6%

A sum of money placed at compound interest doubles itself in 5 years. In how many years it would be 8 times of itself at the same rate of interest?

(A) 10 years

(B) 15 years

(D) 7 years

A sum of money at compound interest amounts to Rs.650 at the end of the first year and Rs.676 at the end of the second year. The sum of money is

(A) Rs.600

(B) Rs.620

(D) Rs.625

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The average of first ten prime numbers which are odd is

(A) 12.9

(B) 13.8

(C) 15.8

(D) 17

The average of first 10 even numbers is

(A) 18

(B) 22

(D) 11

The average age of three boys is 15 years and their ages are in proportion 3: 5:7. What is the age in years of the youngest boy?

(A) 15

(B) 9

(D) 21

26. In an Arithmetic Progression, if a = 28, d = -4, n = 7, then an is :

(A) 4

(B) 5

(D) 7

The age of son today is 1/4 th of the age of his father. After 20 years, age of father will be twice the age of his son. The age of the father today is

(A) 36

(B) 40

(D) 48

Amal and Bimal started a business. Amal invested Rs.500 for 9 months and Bimal invested some money for 6 months. If they make a profit of Rs.69 in a year and Bimal gets profit share of Rs.46. The capital of Bimal in the business is

(A) Rs.1,500

(B) Rs.3,000

(D) Rs.6,000

A farmer has some hens and some rabbits. If the total number of the feet of the hens and the rabbits is 160 and their total number of heads is 50, the numbers of hens the farmer have

(A) 20

(B) 18

(D) 15

If x is a prime number, the LCM of x and (x + 1) is

(D)

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Through the publicity of road safety programmes the street accident in a state has been decreased by 10% in comparison to its previous year. In the present year, if the number of street accidents be 2187, the number of street accidents that had been in the state 3 years before is

(A) 4000

(B) 2430

(C) 3000

(D) 1458

Two trains running in opposite direction cross a man standing on the platform in 27 secs and 17 secs respectively and they cross each other in 23 secs. The ratio of their speeds is

(A) 1:3

(B) 3:2

(D) 3:4

The average of first 10 odd numbers is _________ .

(A) 11

(B) 10

(D) 17

The time in which Rs.80,000 amounts to Rs.92,610 at 10% per annum compound interest, interest being compounded semi-annually, is

(A) 1.5 years

(B) 2 years

(D) 2.5 years

stands for division, stands for multiplication, ‘x’ stands for subtraction and stands for addition. Which of the following equations is correct?

(A) 18÷6-7+5×2 = 20

(B) 18+6+7×5-2 = 18

(D) 18÷6×7+5-2 = 22

A man saved Rs. 16,500 in 10 years. In each year after the first year he saved Rs. 100 more than he did in the preceding year. How much did he save in the first year?

(A) Rs. 1,200

(B) Rs. 1,650

(D) Rs. 1,020

HCF of the fractions

(A) 48/105

(B) 2/105

(D) 1/105

It has been seen in a survey of a region that 70 persons read English newspaper, 73 persons read Bengali newspaper and 64 persons read both the papers. If 63 persons do not read any paper on how many people the survey has been done?

(A) 79

(B) 142

(D) 143

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The least number which when diminished by 5 is divisible by each of 21, 28, 36, 45 is

(A) 425

(B) 1260

(C) 1265

(D) 1259

If the product of two successive positive integers is 7482. Which is the greatest integer?

(A) 87

(B) 82

(D) 89

Find the largest possible number that may divide each of two numbers sum of which is 1394, when none of the component numbers is zero or equal to each other.

(A) 17

(B) 34

(D) 82

A trader mixes three varieties of groundnuts costing Rs.50, Rs.20 and Rs.30 per kg in the ratio 2:4:3 in terms of weight and sells the mixture at Rs.33 per kg. What percentage of profit does he make?

(A) 8%

(B) 9%

(C) 10%

(D) None of the above

There are five positive observations. Average of the first three observations is 8 and that of the last three observations is 6. If the average of all five observations is 6, what is the third observation?

(A) 10

(B) 8

(C) 12

(D) 14

A single person takes 6 minutes to fill a bottle. If from 11 am to 12.30 pm 1845 bottles are to be filled, how many persons should be employed on this job?

(A) 121

(B) 127

(C) 123

(D) 139

A plot of 640 sq ft is available at the rate of Rs.4,600 per sq ft. If 30% of the total cost of the plot is to be paid for booking the plot. How much is the booking amount?

(A) Rs.9,38,100

(B) Rs.8,83,200

(D) Rs.8,38,100

If a car is sold for Rs.50,000 the profit is 17 per cent, what would be profit percentage if sold for Rs.47,000?

(A) 14.85%

(B) 9.98%

(D) 14.50%

A man borrowed Rs.16,000 from two persons. He paid 6% interest per annum to one and 10% interest per annum to the other. In the first year he paid a total interest of Rs.1,120. How much did he borrow from the first and second person respectively?

(A) Rs.12,500; Rs.3,500

(B) Rs.11,000; Rs.5,000

(C) Rs.12,000; Rs.4,000

(D) Rs.10,000; Rs.6,000

Find the largest possible 4 digit number divisible by 45. 18 and 35.

(A) 9540

(B) 9450

(D) 9350

The HCF of two numbers is 4 and LCM is 520. If one of the numbers is 52, the other number is then,

(A) 40

(B) 42

(D) 50

In a two digit number, the unit’s digit exceeds ten’s digit by 2 and the product of the sum of the digits and the number is 144, then what is the number?

(A) 24

(B) 02

(D) 46

A survey shows that 73% of the Indians like apples, whereas 65% like oranges. What percentage of Indians like both apples and oranges?

(A) 83%

(B) 8%

(C) 38%

(D) 35%

Which term of the A.P. 3, 8, 13, 18, …… is 78?

(A) 12th

(B) 13th

(D) 16th

A milkman has 21 litres of whole milk, 42 litres of toned milk and 63 litres of double toned milk. If he wants to pack the three types of milk in cans so that in no can two types of milk are mixed, then what is the minimum number of can would he require?

(A) 12

(B) 9

(C) 6

(D) 3

A man borrows Rs.2,550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be?

(A) Rs.1,352

(B) Rs.1,283

(D) Rs.1,275

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Total price of 6 shirts and 7 trousers is Rs.4,130 while that of 4 shirts and 9 trousers is Rs.4,270. Find out the price of 3 shirts.

(A) Rs.850

(B) Rs.840

(D) Rs.810

The maximum number of students among whom 910 pens and 1001 pencils can be distributed in such a way that each student gets same number of pens and pencils, is

(A) 1911

(B) 910

(D) 91

∛0.000216

(A) 0.6

(B) 0.006

(C) 0.06

(D) 0.0006

If 17th term of an A.P. exceeds its 10th term by 7. The common difference is

(A) 1

(B) 2

(D) 4

The least number which when divided by 15, 27, 35 and 42 leaves a remainder of 7 in each division is

(A) 1883

(B) 2007

(C) 1897

(D) 1987

Masood purchased a plot for Rs.8,000. He sells the plot to Aftab at a profit of 20%. Aftab in turn sells that plot to Zahid at a loss of 20%. The plot costs Zahid

(A) Rs.12.000

(B) Rs.10.000

(D) Rs.7680

A pump can fill a tank with water in 2 hours. Because of a leak developed in the tank, it takes now 2.5 hours. to fill the tank. The leak will empty the full tank with pump not running, in

(A) 8 hours

(B) 10 hours

(D) 2.33 hours

The sum of the first five multiples of 3 is

(A) 45

(B) 55

(D) 75

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If & + 2& + && + 1&&= 2 & 4 then & stands for

(A) 5

(B) 6

(D) 8

A person runs for 1 hour, 1 hour, 1.5 hours and 1.5 hours, respectively, along the sides of a square track. If length of each side is 20km, then his average speed in km/hour is

(A) 16

(B) 22

(D) 26

A lift carrying 50 passengers from the ground floor of a 100 storied building is moving upward. The lift stops at 1st, 2nd, 3rd floor then skips 4th floor, again stops at 5th, 6th and 7th then skips 8th floor and so on. Passengers get discharged in a pattern. 2, 3, 3, 2, 3, 3, In which floor the lift becomes empty?

(A) 16

(B) 24

(C) 25

(D) 26

The smallest number which when divided by 12, 15, 20 or 54 leaves a remainder of 4 in each case, is

(A) 454

(B) 564

(C) 544

(D) 464

If √529 = 23 then the value of √0.000529 is

(A) 2.3

(B) 0.23

(C) 0.023

(D) 0.0023

Total expenses of a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders are 120 and 100 the total expenses are Rs.2000 and Rs.1700 respectively. Find the total number of boarders if the total expense is Rs.1880.

(A) 200

(B) 112

(D) 115

The average of first 10 natural numbers is

(A) 5

(B) 5.5

(D) 6

A boatman can row a boat downstream and upstream at 13 kmph and 9 kmph respectively. What will be the speed of boat in still water? (in kmph)

(A) 12

(B) 10.5

(C) 11

(D) 10

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If the ratio of three numbers are 3:4:5 and their LCM is 1200, then the smallest number is

(A) 80

(B) 60

(D) 100

The missing terms in A.P.: ___, 13, ___, 3 are

(A) 11 and 9

(B) 17 and 9

(C) 18 and 8

(D) 18 and 9

Find the least possible 5 digit number dividing which by each of 12, 10, 16 and 18 leaves a remainder of 5.

(A) 10105

(B) 10055

(C) 10085

(D) 10155

A certain sum of money amounts to Rs.1,680 in 3 years and to Rs.1,800 in 5 years. Find the sum and rate of simple interest.

(A) Rs.1,200 ; 4%

(B) Rs.1,500 ; 4%

(D) Rs.1,600 ; 5%

A is twice as good a workman as B. A and B together complete a piece of work in 28 days. In how many days will A alone do the same piece of work?

(A) 40 days

(B) 42 days

(D) 36 days

If an amount of Rs.84,105 is distributed equally amongst 35 children. How much amount would each child get?

(A) Rs.2,430

(B) Rs.2,043

(C) Rs.2,403

(D) None of the above

Gold is 19 times as heavy as water and copper is 9 times as heavy as water. The ratio in which these two metals are to be mixed so that the mixed alloy becomes 15 times as heavy as water is

(A) 2:3

(B) 1:2

(C) 3:2

(D) 19:135

The least number that is to be subtracted from 5629 to make the result a perfect square is

(A) 4

(B) 1

(D) 3

Which of the following is the value of

(A) 360

(B) 400

(D) 420

The number of multiples of 4 between 10 and 250 is

(A) 50

(B) 40

(C) 60

(D) 30

In a class of 150 students 70 passed in mathematics, 60 students passed in statistics and 20 in both subjects. Then number of students failed in both subjects is

(A) 30

(B) 40

(D) 60

A man makes a profit of 20% on selling 20 articles for Rs.1. The number of articles he bought by Rs.1 is

(A) 24

(B) 20

(D) 30

Find the compound interest on Rs.14,000 for 2 years at 5%, interest being payable annually

(A) 15,435

(B) 1,435

(D) 1,535

The difference of a proper fraction and its reciprocal is 7/12. Find the fraction.

(A) -4/3

(B) 3/4

(D) 1/2

Income of X is 25% more than that of the income of Y. What per cent is Y’s income less than that of X’s income?

(A) 25%

(B) 24%

(C) 20%

(D) 22.5%

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How much time will it take for an amount of Rs.450 to yield Rs.81 as interest at 4.5% per annum of simple interest?

(A) 3.5 years

(B) 4 years

(D) 5 years

10²+1/100 + 0.0001 equals to

(A) 1.000101

(B) 10.00101

(C) 100.0101

(D) None of the above

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is

(A) 53.33

(B) 54.68

(D) None of the above

The difference between the compound interest and the simple interest at the same rate of interest, for the amount Rs.5,000 in 2 years, is Rs.32. The rate of interest is

(A) 5%

(B) 10%

(D) 8%

Five bells ring at intervals of 3, 5, 6, 8, and 9 seconds. If all the bells ring once, after how long a period the bells would ring together again?

(A) 12 minutes

(B) 6 minutes

(D) 24 minutes

Which is the greatest?

(A) √0.09

(B) ∛0.064

(C) 3/5

(D) 0.5

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If A and B complete a job working together in 20 days, B and C together in 15 days and C and A in 12 days, all three working together will be able to complete the same job in,

(A) 9 days

(B) 10 days

(D) 6 days

The sum of first 16 terms of the A.P.: 10, 6, 2,… is

(A) -320

(B) 320

(D) -400

The present age of Neha and Rashmi are in the ratio of 7:8 respectively. Six years later, the ratio of their ages will become 9:10 respectively. What is Rashmi’s present age?

(A) 36

(B) 24

(D) 40

Which of the following ratios is greatest?

(A) 7:15

(B) 15:23

(D) 21:29

The value of

(A) 2

(B) 4

(D) 8

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Solution by SmartMaths

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WBCS Main Question Paper – 2020

2. Raju invested Rs. 15,000 in two parts. One part on 8% and other at 12% per annum. His annual income is Rs. 1640. Ratio of the two parts respectively

(A) 3 : 7

(B) 5 : 9

(D) 7 : 11

4. Successive discounts of x% and y% are equivalent to a single discount of

(A) (x+y) %

(B) x+y/2 %

(D) x−y/2 %

5. Gold and Copper are heavier than water by 19 and 9 times respectively. In what proportion should they be mixed to form an alloy so that it will be heavier than water by 15 times ?

(A) 1 : 2

(B) 2 : 3

(D) 3 : 2

8. The marked price of a pen is Rs.200 and a customer buy it for Rs.153 after two successive discounts. If first is 10%, then the second is

(A) 20%

(B) 18%

(D) 15%

11. Rahul’s salary is first increased by 10% and then again by 20%. But due to covid the salary is decreased by 25%. By what per cent the initial salary changes ?

(A) 1% increased

(B) 1% decreased

(D) 2% decreased

16. Sneha wants to buy a furniture worth Rs. 12,500, she gets a discount of 10% on it. After getting the discount, she pays 18% GST. Find the amount she will have to pay for the furniture.

(A) Rs. 12,540

(B) Rs. 13,125

(D) Rs. 14,250

30. Barun invests Rs. 5000 for a year and Tarun joins him with Rs. 8000 after six months. After the year they receive a return of Rs. 4500, then Tarun’s share is

(A) Rs. 2000

(B) Rs. 2500

(D) None of the above

33. The income of Priya is 40% higher than that of Liza and the income of Disha is 20% less than that of Liza. Income of Priya is higher than income of Disha by

(A) 25%

(B) 75%

(D) None of the above

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35. Present ages of Ram and Laxman are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Laxman’s present age ?

(A) 24 years

(B) 27 years

(D) 30 years

37. In an examination, 34% of the candidates fail in Bengali and 42% in English. If 20% fail in Bengali and English, the percentage of those passing in both subjects is

(A) 44

(B) 45

(D) 47

38. Mohit went to a shop to buy 50 kg of rice. He buys two varieties of rice which cost him Rs.4.50 per kg and Rs.5 per kg. He spends a total of Rs.240. What was the quantity of less expensive rice bought by him ?

(A) 20 kg

(B) 25 kg

(D) 35 kg

39. The ratio of syrup and water in 30 litre of a mixture is 1 : 5, then the amount of water required to mix to make the ratio 1 : 6 is

(A) 3 litres

(B) 4 litres

(D) 6 litres

40. In an examination 75% passed in Maths, 80% passed in Bengali, 65% in both and 45 students failed in both subjects . Then the number of students appeared are

(A) 400

(B) 500

(D) None of the above

43. Satyajit is younger than Diganta by 8 years. If their ages are in the ratio of 5 : 7, then how old is Satyajit ?

(A) 18 years

(B) 22 years

(D) 20 years

53. The price of sugarcane rises by 20%. Then by how much per cent does a housewife reduce her consumption so that her expenditure remains same ?

(A) 162/3%

(B) 20%

(D) 121/2%

55. In an election 15% of voters did not vote. Ratanbabu got 62.5% of votes cast was declared elected by 3400 votes. Then the total number of votes are

(A) 15000

(B) 16000

(D) 19000

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12. A man buys two types of oranges equal in number one at 5 for a rupee and the other at 3 for a rupee and sells the whole at 6 for Rs. 2, then his gain or loss per cent is

(A) 25% gain

(B) 20% loss

(D) 25% loss

20. A man buys milk at Rs.60 per litre, adds water to it and then sells it at Rs.50 per litre. What is the ratio of milk and water if his profit in the deal is 20% ?

(A) 5 : 9

(B) 25 : 11

(D) 13 : 16

21. Avishek sells a book at a profit of 20%. If he had bought it at 20% less and sold it for Rs. 18 less, he would have gained 25%.The cost price of the book is

(A) Rs.80

(B) Rs.70

(D) Rs.90

24. Rs.6000 is divided among 40 boys and some girls so that each boy gets Rs.100 and each girl gets Rs.250, then the number of girls is

(A) 20

(B) 15

(D) 9

29. Rohit sold two books at Rs.60 each. On one he gains 20% and on the other loses 20%. Then he made

(A) no profit no loss

(B) loss of 4%

(D) loss of 1%

28. Average age of 8 sons of a family is 12 years. Average age of the sons together with their parents is 21 years. If the father is older than the mother by 8 years, then the age of the mother is

(A) 48 years

(B) 53 years

(D) 62 years

44. The mean of five observations x, x + 2, x + 6, x + 4, x + 8 is 11. The mean of last three observations is

(A) 9

(B) 9.33

(D) 9.66

47. A merchant purchases 11 toys for Rs.10 and sold 10 toys for Rs.11. His profit is

(A) 45%

(B) 20%

(D) 25%

49. An article is sold at Rs. 972, then profit is 8%. If it is sold at Rs. 872, then there is a loss of

(A) Rs. 28

(B) Rs. 25

(D) Rs. 15

52. The income from a bus in every trip is Rs.100. If the bus fare increases by 50% and the number of passengers decreases by 20%, then the income in every trip is

(A) Rs. 120

(B) Rs. 80

(D) Rs. 110

54. The cost price of an article A is Rs.200 and selling price of another article B is Rs.308. If the selling price of A will be equal to the cost price of B, then the profit after selling A is 10%. What is the profit on B ?

(A) 20%

(B) 30%

(D) 50%

1. 8 men or 12 women can do a piece of work in 20 days. The number of days needed to complete the job, if 10 men and 15 women are employed to do the same piece of work is

(A) 10

(B) 15

(D) 20

10. A bus travels from Kolkata to Digha at the rate of 55 km/hour and returns at the rate of 66 km/hour. Then the average rate of the whole journey is

(2xy/x+y)

(A) 50 km/hour

(B) 55 km/hour

(D) 72km/hour

13. A train travels at a speed of 30 km/hour for 12 minutes and then for the next 8 minutes at a speed of 45 km/hour, then the average speed for the journey is

(A = D/T)

(A) 36 km/hour

(B) 39 km/hour

(D) 42 km./hour

18. A pipe can fill a tank in 16 hours. Due to a leak in the bottom, it’s filled in 24 hours. If the tank is full, how much time will the leak take to empty it ?

(A) 36 hours

(B) 42 hours

(D) 48 hours

19. A man travels three-fifth of a distance AB at a speed 3x and the remaining at a speed 2y. If he goes from B to A and returns at a speed 5z in the same time, then which one is correct ?

(A) 1/x + 1/y = 1/z

(B) x + y = z

(D) x + z = y

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42. If the time taken to go from one station to other is required to be decreased by 20% then by what per cent the speed of the train will have to be increased ?

(A) 20%

(B) 25%

(D) 12%

58. The speed of a boat in still water is 8 km/hour. If it can travel 20 km downstream and 12 km upstream at the same time, the speed of the stream is

(A) 2 km/hour

(B) 2.5 km/hour

(D) 3.5 km./hour

3. If a sum of money doubles itself at compound interest in 12 years. In how many years will it become four times ?

(A) 26 years

(B) 24 years

(D) 18 years

6. The compound interest on Rs.10,000 in 21/2 years at 10% per annum is

(A) Rs. 2010

(B) Rs. 2250

(D) Rs. 2833

25. A man gets a simple interest of Rs.3500 on a certain principal at the rate of 10% per annum in 5 years. What compound interest will the man get on twice the principal in two years at the same rate ?

(A) Rs. 2520

(B) Rs. 1750

(D) Rs. 2940

27. The simple interest and compound interest of a certain sum of money for two years are Rs.400 and Rs.410 respectively. Then the rate of interest per annum is

(A) 5%

(B) 6%

(D) 6.5%

48. A sum of money lent by Jadu at simple interest becomes double of itself in 8 years. Then the sum will, triple itself in

(A) 16 years

(B) 15 years

(D) 24 years

26. If the first and second of the five numbers in continued proportion are 2 and 8 respectively, then the fifth number is

(A) 512

(B) 16

(D) 256

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23. Ram and Shyam solve a quadratic equation. Ram makes a mistake in the constant term and finds the roots as 5, -3. Shyam makes a mistake in the co-efficient of x gets the roots as 1, -3. The correct roots are

(A) 1, 3

(B) -1, 3

(D) 1, -1

51. Simplified value of

(A) 984762

(B) 984763

(D) 1

62. The age of father today is thrice as that of his son. After 15 years, the age of the father will be twice that of his son. The age of the son today is

(A) 12 years

(B) 15 years

(D) 24 years

65. The price of coal being increased by 20%, family reduce the consumption of coal by 20%. Then how much per cent will the family’s expenses for coal be increased or decreased ?

(A) No change

(B) 4% increased

(D) 3% decreased

66. Ranjan sold his bag to Joydip at a gain of 8% and Joydip sold it to Raju at a gain of 10%. If Raju paid Rs. 297 for it, the price paid by Ranjan is

(A) Rs. 250

(B) Rs. 260

(D) Rs. 280

68. While preparing mixture of tea, 5% tea is lost. In what ratio a trader should mix two kinds of tea costing Rs.600/kg and Rs.450/kg respectively so that he might gain 25% on selling the mixed tea at Rs.625/kg ?

(A) 3 : 5

(B) 4 : 5

(D) 1 : 5

73. A person walks from his house at a speed of 4 km/hour and reaches his school 5 minutes late. If his speed has been 5 km/ hour he would have reached 10 minutes earlier. The distance of the school from his house is

(A) 5 km

(B) 6 km

(D) 8 km

76. The radius and height of a cone are each increased by 10%, then the volume of the cone is increased by

(A) 21%

(B) 33.1%

(D) 30.4%

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78. If the cost price of 12 articles is equal to selling price of 10 articles, then percentage of profit is

(A) 25%

(B) 30%

(D) 20%

81. A number is increased by 10% and then decreased by 10%, then the number

(A) doesn’t change

(B) decreases by 1%

(D) None of the above

82. A man invests Rs.5000 at a rate of 6% per annum. How much more should he invest at a rate of 9%, so that he can earn a total of 7% per annum ?

(A) Rs.5000

(B) Rs.2500

(D) Rs.4500

83. A sum of money compounded annually becomes Rs.500 in two years and Rs.550 in three years. The rate of interest per annum is

(A) 8%

(B) 10%

(D) 15%

85. If the rate of compound interest for the first year is 4% and second year is 5%, then the compound interest on Rs.25,000 for 2 years is

(A) Rs.2000

(B) Rs.2300

(D) Rs.2500

86. A and B can do a piece of work in 10 days, B and C in 12 days, C and A in 15 days, then that numbers of days taken by A, B and C together to finish the work are

(A) 6 days

(B) 8 days

(D) 18 days

87. Pipe A can fill a tank in 3 hours and pipe B can fill it in 4 hours. If they are opened at alternate hours and if pipe A is opened first, in how many hours will the tank filled ?

(A) 3¼ hours

(B) 4 hours

(D) 3⅓ hours

88. Six years hence, a man’s age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

(A) 28 yrs

(B) 30 yrs

(D) 34 yrs

89. 76 ladies can do a job in 33 days. Due to some reason, some ladies did not join the work and therefore, it was completed in 44 days. The number of ladies who did not join the work is

(A) 22

(B) 21

(D) 19

90. In a joint business, ratio of the capitals of three friends was 1212 : 13:13: 1212. After 4 months the first friend withdrew half of his capital and 8 months thereafter Rs. 2024 was recorded as their total profit. What was the share of profit of the first friend ?

(A) Rs. 542

(B) Rs. 672

(D) Rs. 816

91. The difference between simple interest and compound interest on a sum for 3 years at 10% when the interest is compounded annually is Rs. 155. Then the principal value is

(A) Rs. 4000

(B) Rs. 5000

(D) Rs. 6000

92. The current population of a town is 120000. If the population increases by 10% every year, then the population of the town after three years will be

(A) 125550

(B) 162900

(D) 159720

95. Out of 15 cows one worth Rs.1800 was removed and a horse was taken in. If their average price is thereby increased by Rs.300, then the price of the horse is

(A) Rs.6000

(B) Rs.6300

(D) None of the above

96. The production of scooters rose to 48400 from 40000. If rate of growth is 10%, then the time required

(A) 5 years

(B) 4 years

(D) 2 years

98. Amal invests 1/4 of his capital at 8% p.a., 1/5 at 10% p.a. and the remainder at 7% p.a. If his annual income is Rs.628, then the capital is

(A) Rs. 7500

(B) Rs. 7700

(D) Rs. 8500

100. A manufacturer marked an article at Rs.120 and sold it allowing 15% discount. If his profit was 20%, then the prime cost of the article is

(A) Rs.85

(B) Rs.90

(D) Rs.110

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101. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water ?

(A) 40 mins

(B) 1 hour

(D) 1 hr 30 mins

103. What fraction of 4/7 must be added to itself to make the sum 15/14 ?

(A) 1/2

(B) 4/7

(D) 15/14

104. A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is

(A) 2.5 kmph

(B) 4.2 kmph

(D) 10.5 kmph

107. Jaya and Hima are competing in a 200 meter race. Both start the race at the same time, but Jaya starts the race 40 meters ahead of the starting point, whereas Hima starts the race at the starting point. Assume that Hima runs at a speed of 10 meters per second, whereas Jaya runs at a speed of x meters per second. If both reach the finish line at the same time, then what is the value of x ?

(A) 8 meters per second

(B) 10 meters per second

(D) 2 meters per second

109. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is

(A) 9

(B) 11

(D) 15

113. A and B are at a distance of 800 m. They start towards each other at 20 and 24 kmph. As they start a bird sitting on the cap of A, starts flying towards B, touches B and then returns towards A and so on, till they meet. What is the distance travelled by the bird, if its speed is 176 kmph ?

(A) 3040 m

(B) 3200 m

(D) 2600 m

114. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water ?

(A) 4 kmph

(B) 6 kmph

(D) Data inadequate

115. When a number is added to seven-ninth of thirty-five per cent of 900, the resultant is 325. What is the number ?

(A) 81

(B) 80

(D) 60

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118. A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is

(A) 1/2

(B) 1

(D) 2

119. If one-third of a tank hold 80 litres of water, then the quantity of water that half of the tank holds is

(A) 80/3 litre

(B) 100 litre

(D) 240 litre

121. A shopkeeper gives two successive discounts of 20% and 10% on surplus stock. Further, he also gives 5% extra discount on cash payment. If a person buys a shirt from the surplus stock and pays in cash, what overall discount percent will he get on the shirt ?

(A) 60%

(B) 5.67%

(D) 2%

123. A person travels 3.5 km from place A to place B. Out of this distance, he travels 5/3 km on bicycle, 7/6 km on scooter and the rest on foot. What portion of the whole distance does he cover on foot ?

(A) 3/9

(B) 4/11

(D) 5/6

125. When a ball bounces, it rises to 3/4 of the height from which it fell. If the ball is dropped from a height of 32 m, how high will it rise at the third bounce ?

(A) 13 m

(B) 13.5 m

(D) None of the above

134. If the current ratio of the father’s age to the son’s age is 4 : 1 and the product is 256, what will be the ratio of ages after 5 years ?

(A) 37 : 13

(B) 38 : 12

(D) 50 : 1

140. What is the smallest number which when decreased by 8 is divisible by 21, 27, 33 and 55 ?

(A) 1490

(B) 10405

(D) None of the above

145. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?

(A) 76 kg

(B) 5 kg

(D) None of the above

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146. The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

(A) 4

(B) 8

(D) None of the above

148. A sum of Rs.312 was divided among 100 boys and girls in such a way that each boy gets Rs.3.60 and each girl Rs.2.40. The number of girls is

(A) 40

(B) 45

(D) 30

149. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is

(A) 18

(B) 24

(D) 81

150. How many numbers between 400 and 600 begin with or end with the digit 5 ?

(A) 40

(B) 100

(D) 120

151. Suppose milk is sold at the rates of 5.50, 6.00, 5.75 and 5.25 rupees per litre in four different months. Assuming that equal amount of money are spent on milk by a family in the four months, the average price in rupees per litre will be

(A) 5.61

(B) 5.62

(D) 5.64

152. A car is running first 5 kilometers at a speed of 40 km./hr., next 20 kilometers at 60 km./hr. and then another 30 kilometers at 50 km./hr. speed. Then the average speed of the car is

(A) 51.97 km./hr.

(B) 50 km./hr.

(D) 50.6 km./hr.

154. In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is

(A) 3

(B) 5

(D) 9

155. A tap can fill a bucket in 6 hours. After half the bucket is filled, three more similar taps are opened. What is the total time taken to fill the bucket completely ?

(A) 3 hrs 15 mins

(B) 3 hrs 45 mins

(D) 4 hrs 15 mins

158. A whole number n which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?

(A) 0

(B) 1

(D) 2

168. If one-third of one-fourth of a number is 15, then three-tenth of that number is

(A) 35

(B) 36

(D) 54

173. Sanket earns twice as much in the month of March as in each of the other months of the year. What part of his entire annual earnings was earned in March ?

(A) 1/7

(B) 1/6

(D) 2/13

174. If the average of a, b, c is 15, the average of b, c, d is 12 and the average of a, d is 13, the value of d is

(A) 34

(B) 30

(D) 10

175. Raju, Ramu and Razi can do a piece of work in 20, 30 and 60 days respectively depending on their capacity of doing work. If Raju is assisted by Ramu and Razi on every third day, then in how many days Raju will complete the work ?

(A) 12 days

(B) 15 days

(D) 18 days

180. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number ?

(A) 3

(B) 4

(D) Cannot be determined

182. If [4.5] = [4+0.5] = 4, then [- 4.5] will be

(A) – 4

(B) 4

(D) – 5

184. What is the number of digits in (3³)³ ?

(A) 4

(B) 5

(D) 7

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190. What fraction of an hour is a second ?

(A) 1/24

(B) 1/60

(D) 1/3600

194. A reduction of 20% in the price of strawberries enables a person to purchase 12 more for Rs.15. What was the price of 16 strawberries before reduction of price ?

(A) Rs.6

(B) Rs.5

(D) Rs.9

197. The unit’s digit present in the product 274 x 318 x 577 x 313 is

(A) 2

(B) 3

(D) 5

198. The digit in unit’s place of the product 81 x 82 x … x 89 is

(A) 0

(B) 2

(D) 8

Video Solution

Solution by SmartMaths

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WBCS Main Question Paper – 2019

1. The ratio of bus and train fares from Burdwan to a certain place is 3 : 4. If the train fare increases by 20% and bus fare by 10% then what will be the new ratio of bus and train fares ?

(A) 12 : 23

(B) 11 : 16

(D) 16 : 15

2. When the price of rice increases 121/2 %, a man can get 250 gm less rice for Rs.18. Find the present cost of rice per kg.

(A) Rs. 8

(B) Rs. 7

(D) Rs. 7.50

3. Of four numbers, the second number is 20% more than the first, the third is 10% less than the second and the fourth number is 50% more than the third. If the fourth number is 405, find all the numbers.

(A) 300, 405, 250, 270

(B) 300, 270, 405, 250

(D) 250, 300, 270, 405

4. The expense for rice, fish and oil of a family are as 12 : 17 : 3. The prices of these articles are increased by 20%, 30% and 50% respectively. By what percent the expenses for these articles of the family will be increased ?

(A) 27 1/8%

(B) 27 1/7%

(D) 29 1/8%

5. In a certain examination, a candidate answered 25 questions and two-fifth of the rest of the total number of questions and he found that thus he has answered only 60% of the total number of questions. How many questions did he answer ?

(A) 45

(B) 40

(D) 65

6. A man saves 20% of his income. If his expenses be increased by 35%, by what percent his income is to be raised so that he can save 10% of his income ?

(A) 20%

(B) 30%

(D) 22%

7. A mixture of milk and water contains 121/2 % of water. How much water should be added to 200 gallons of such mixture so that the new mixture may contain 371/2 % of water ?

(A) 70 gallons

(B) 100 gallons .

(D) 80 gallons

8. One litre of spirit which contains 10% of water is added to 3 litres of spirit containing 7% of water and to this mixture half a litre is added. Find the percentage of water in the final mixture.

(wrong question)

(A) 15%

(B) 18%

(D) 22%

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9. A certain kind of brass is composed of copper, zinc, lead and tin, the ratio of copper to zinc is 1 : 2 of zinc to lead is 3 : 5 and of lead to tin is 7 : 8. Find the quantity of each metal in 213 gm brass.

(A) 21 gm, 42 gm, 70 gm, 80 gm

(B) 20 gm, 40 gm, 70 gm, 80 gm

(D) 22 gm, 40 gm, 60 gm, 80 gm

14. 1200 boys and 600 girls are examined in a test. 42% of the boys and 30% of the girls passed. Find the percentage of those who failed ?

(A) 62%

(B) 70%.

(D) 80%

99. The ratio of two numbers is 3 : 4 and their L.C.M. is 180. Find the numbers.

(A) 45, 60

(B) 40, 25

(D) 30, 60

100. The ratio of two numbers is 5 : 8 and their difference is 69. Find the numbers.

(A) 120, 131

(B) 150, 163

(D) 118, 173

63. A invested Rs.6000 for 5 months and B Rs.5000 for x months in a business. If the profit of A and B be equal, find the value of x.

(A) 10 months

(B) 8 months

(D) 7 months

64. Two friends start a business with the capitals Rs.16,000 and Rs.24,000. They make a profit of Rs.3375 in a year. How much each friend will get as a part of the profit ?

(A) Rs.1350, Rs.2025

(B) Rs.1525, Rs.2225

(D) Rs.1250, Rs.2225

65. Three friends P, Q and R started a business with the capitals Rs.15,000, Rs.10,000 and Rs.25,000. But at the end of the year, they suffer a loss of Rs.25,000. How much each will have to pay for the loss ?

(wrong options)

(A) Rs. 500, Rs. 750 and Rs. 1000

(B) Rs. 750, Rs. 500 and Rs. 1250

(D) Rs. 1000, Rs. 500 and Rs. 700

66. At the starting of the year X and Y jointly start a business with Rs.24,000 and Rs.30,000. After 5 months A invests Rs. 12,000 more in the business. At the end of the year if the profit in the business is Rs.14,030, find the part of the profit of each of them.

(A) Rs.8130, Rs.5900

(B) Rs.9130, Rs.4900

(D) Rs.6130, Rs.7900

67. X and Y Jointly start a business with Rs.1200 and Rs.800. At the end of the year Y gets Rs,120 as profit. As a part of profit X will get

(A) Rs.200

(B) Rs.180

(D) Rs.150

68. X, Y and Z start a business with Rs.7200. After 1 year X, Y and Z get Rs.60, Rs.90 and Rs.120 as profit. Z invests an amount

(A) Rs.1800

(B) Rs.2400

(D) Rs.3200

69. Mr. X invests Rs.600 for 5 months and Y invests Rs.500 for 9 months in a business. The part of the profit will be distributed among them in the ratio.

(A) 3 : 2

(B) 4 : 3

(D) 2 : 3

70. In a partnership business the total profit of A and B is Rs.2000. If the capital of A is Rs.6000 and profit is Rs.1200, then the capital of B is

(A) Rs.4000

(B) Rs.5000

(D) Rs.3000

71. In a joint business X invests Rs.6000 for 9 months and Y invests Rs.8000 in some months. They get Rs.1800 and Rs.1600 as profit. In the business, the investment of Y was for

(A) 4 months

(B) 5 months

(D) 8 months

72. In a joint business the capitals of A and B are in the ratio 3 : 4 and the capitals of B and C are in the ratio 6 : 5. If A gets a profit of Rs.450, find the profit of C.

(A) Rs.400

(B) Rs.500

(D) Rs.450

73. In a joint business the capitals of P, O and R, are in the ratio 1/4:1/3:1/2. At the end of the year they make a profit of Rs.3900. Find how much of the profit C will get

(A) Rs.2000

(B) Rs.1500

(D) Rs.1800

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76. In a business P invests Rs.12,000. After some days Q joins the business and invests Rs.16,000 in it. 9 months after Q joins, P and Q get same profit. Find for how many months P’s money was invested in the business.

(A) 20 months

(B) 11 months

(D) 10 months

#wrong solution in video

77. P starts a business with capital of Rs.5000. After 3 months Q joins in the business with capital Rs.6000 and after 5 months R invests Rs.8000 in the business. At the end of the year of the profit is Rs.3400, how much money each will get ?

(A) Rs. 1200, Rs.1080 and Rs.1120

(B) Rs.1200, Rs.1100 and Rs.1000

(D) Rs.1200, Rs.900 and Rs.1100

78. S and T start a business with Rs.2400 and Rs.1600. After one year if S suffers a loss of Rs.45 in the business, then loss of T is

(A) Rs.25

(B) Rs.30

(D) Rs.42

79. P and Q start a joint business. P invests Rs.500 for 9 months and Q invests some money in the business for 6 months. The total profit in the business is Rs.69 and Q gets a profit of Rs.46. The capital of Q in the business is

(A) Rs.1500

(B) Rs.3000

(D) Rs.6000

80. In a joint business the ratio of the capitals of three partners is 5 : 7 : 9. If the profit in the business is Rs.420, then the third partner will get

(A) Rs.100

(B) Rs.140

(D) Rs.200

81. A and B are equal partners. They admit C and D as partners with 1/5th and 1/6th share respectively. What is the profit sharing ratio of all the partners ?

(A) 19 : 19 : 12 : 10

(B) 21 : 19 : 13 : 9

(D) 19 : 17 : 15 : 11 .

82. A and B are partners sharing profits in the ratio of 7 : 3. They admit C for 1/5th share, which he acquires in equal proportions from both. Find the new profit sharing ratio

(A) 2 : 1 : 1

(B) 3 : 2 : 1

(D) 3 : 1 : 1

83. A and B are partners sharing profits in the ratio of 5 : 4. they admit C for 1/9th share, which he acquires from A. Find out the new profit sharing ratio.

(A) 3 : 3 : 1

(B) 2 : 2 : 1

(D) 5 : 5 : 2

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84. X and Y are partners in a firm sharing profits in the ratio of 3 : 2. They admit R as a new partner from 1st April, 2019. X gives 1/3rd of his share while Y gives 1/10th from his share. Calculate the sacrificing ratio.

(A) 3 : 2

(B) 2 : 1

(D) 1 : 2

85. P and Q are partners sharing profits in the ratio of 3 : 2. P surrenders 1/6th of his share and Q surrenders 1/4th of his share in favour of R, a new partner. What is the sacrificing ratio ?

(A) 3 : 2

(B) 2 : 3

(D) 3 : 11

86. S and T are partners sharing profits in the ratio of 3 : 2. W admitted as a partner. The new profit sharing ratio of S, T and W is 4 : 3 : 2. Find out the sacrificing ratio.

(A) 3 : 5

(B) 7 : 3

(D) 3 : 7

87. P and Q were partners sharing profits in the ratio of 3 : 2. They admit R and S as new partners. P surrenders 1/3rd of his share in favour of R and Q surrenders 1/4th of his share in favour of S. Calculate the new profit sharing ratio of P, Q, R and S.

(A) 4 : 3 : 2 : 1

(B) 5 : 4 : 3 : 2

(D) 4 : 4 : 3 : 1

88. A and B are partners sharing profits in the ratio of 7 : 5. They agree to admit C, their manager into partnership, who is to get 1/6th share in profits. He acquires his share 1/24th from A and 1/8th from B. Calculate the new profit sharing ratio.

(A) 13 : 11 : 9

(B) 13 : 7 : 4

(D) 13 : 11 : 5

89. A, B and C are partners in a firm sharing profits in the ratio of 4 : 3 : 2. They admit D as a new partner. A, B and C each surrendered 1/3rd of their shares in favour of D. Calculate the new profit sharing ratio of A, B, C and D.

(A) 8 : 6 : 4 : 9

(B) 8 : 6 : 5 : 4

(D) 8 : 6 : 7 : 9

90. A and B are in partnership sharing profits and losses in the ratio of 3 : 2. They admit C as a new partner. Calculate the new profit sharing ratio if C purchases 1/10th share from A.

(A) 5 : 4 : 3

(B) 4 : 3 : 2

(D) 5 : 4 : 1

91. A and B are partners in a firm sharing profits and losses in the ratio of 5 : 3. They admit C as a partner for 1/4th share in the profits of the firm. Calculate the new profit sharing ratio of A, B and C if C acquires his share 1/5th from A and 1/20th from B.

(A) 17 : 15 : 13

(B) 17 : 13 : 10

(D) 17 :.15 : 10

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98. P’s age is 3/4 of Q’s and R’s age is 11/2 of Q’s age. If the age of R is 30 years, find the age of P.

(A) 10 years

(B) 12 years

(D) 18 years

22. If the ratio of cost price and selling price is 25 : 26, then what is the percentage of profit ?

(A) 4%

(B) 6%

(D) 5%

23. There is some loss if an article is sold at Rs.120. There is same amount of profit if the article is sold of Rs.140. What is the cost price of the article ?

(A) Rs.120

(B) Rs.150

(D) Rs.160

24. A man sold a stove for Rs.423 and incurred a loss of 6%. At what price should it be sold so as to earn a profit of 8% ?

(A) Rs.480

(B) Rs.490

(D) Rs.486

25. A man sold an article at a gain of 5%. Had he sold it for Rs.240 more, he would have gained 8%. Find the cost price of the article.

(A) Rs. 7000

(B) Rs. 9000

(D) Rs.10,000

26. The ratio of manufacturing cost of two sharies is 2 : 5. If the first shari is sold at 15% profit and the second shari is sold at 18% profit then the manufacturer makes a total profit of Rs.396. Find the cost of manufacture of each shari.

(wrong question or options)

(A) Rs.500

(B) Rs.590

(D) Rs.660

27. A book seller allowing 12% discount on the marked price of a book made a profit of 10%. What will be his percentage of profit if he sells the book at the marked price ?

(A) 25%

(B) 30%

(D) 22%

28. A trader sold a bicycle at a profit of 10%. Had he bought the bicycle at 10% less price and sold it at a price Rs.12 more, he would have gained 25%. What is the cost price of the bicycle ?

(A) Rs.500

(B) Rs.480

(D) Rs.450

29. A businessman blends Assam tea costing Rs.70 per kg with Darjeeling tea costing Rs.110 per kg in the ratio 3 : 1. What should be the selling price per kg of the new mixture to have a profit of 121/2% for him ?

(A) Rs.100 per kg

(B) Rs.90 per kg

(D) Rs.80 per kg

30. There is a loss of 11% if an article is sold.at Rs.178. At what price should it be sold to make a profit of 11% ?

(A) Rs. 200

(B) Rs. 220

(D) Rs. 226

31. A retailer getting a discount of 20% on the marked price sells an article at the marked price. Percentage of profit of the retailer is

(A) 10

(B) 20

(D) 30

32. A fruit seller purchased banana at Rs.30 per dozen and sold each pair at Rs.7. What is the percentage profit or loss at this ?

(A) 20% profit

(B) 20% loss

(D) 40% loss

33. Selling a radio at Rs.363.75 there was a loss of 3% of a radio seller. At what price should he sell the radio to make a profit of 10% ?

(A) Rs.400.50

(B) Rs.410.50

(D) Rs.420.50

34. A businessman purchased 35 kg of pulse at Rs.525 and sold each kg at the rate Rs.18. What is his percent of profit or loss at this ?

(A) 20% loss

(B) 20% profit

(D) 25% loss

35. A hawker purchases some mangoes at the rate of 9 mangoes for Rs.5 and sells them at Rs.8 per dozen. What will be his profit or loss percentage ?

(A) 20% loss

(B) 25% profit

(D) 20% profit

36. A businessman sold an article at a loss of 15%. Had he sold the article at Rs.100 more he would have gained 10%. At what price did he sell the article ?

(A) Rs.350

(B) Rs.340

(D) Rs.330

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37. In what ratio should the Assam tea at Rs.40 per kg and Darjeeling tea at Rs.65 per kg be mixed and sold at Rs.60 per kg to make in overall profit of 25% ?

(A) 1 : 2

(B) 2 : 1

(D) 17 : 8

38. A milkman mixed water with 60 litres of pure milk and sold the mixture at the cost price thereby made a profit of 25%. Find the quantity of water in the mixture.

(A) 12 litres

(B) 15 litres

(D) 14 litres

39. A Shoe maker sold two pairs of shoes at the same price. In the first pair he makes a profit of 20% and in the other pair he makes a loss of 20%. What is his percentage of profit or loss in the whole business ?

(A) 3% Loss

(B) 8% Profit

(D) 4% Loss

40. Paban incurred 10% loss by selling lemon at Rs.18 per dozen. At what price should he sell each dozen of lemon to make a profit of 10% ?

(A) Rs.20

(B) Rs.22

(D) Rs.30

41. There is 25% profit if an article is sold at Rs.150. At what per cent should the selling price be increased so that there will be 30% profit ?

(A) 2.5

(B) 4

(D) 10

10. If 25 men can weave 120 metres of cloth in a day, how many metres of cloth will be woven by 35 men in a day ?

(A) 170 metres

(B) 168 metres

(D) 180 metres

11. 12 men can do a piece of work in 30 days. How many extra men should be engaged to do the work in 20 days ?

(A) 8 men

(B) 6 men

(D) 15 men

12. A man and a boy can do a piece of work in 36 days, if the man works alone for the last 10 days, it is completed in 40 days. How long would the boy take to do it alone ?

(A) 85 days

(B) 100 days.

(D) 90 days

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13. A and B together can do a piece of work in 25 days. If B works alone for the last 10 days, it is completed in 30 days. In how many days A alone can do it ?

(A) 50 days

(B) 60. days.

(D) 55 days

15. If 50 men do a piece of work in 12 days working 8 hours a day. How many hours a day would 60 men have to work in order to do another piece of work twice as great in 16 days ?

(A) 10 hours a day

(B) 12 hours a day

(D) 6 hours, a day

16. A contractor undertook to finish a road 12 km long in 350 days. But after employing 45 men for 200 days he found that only 4 km of the road had been built. How many additional men must be engaged to finish the work in the given time ?

(A) 70 men

(B) 80 men

(D) 85 men

17. A laboratory has to pay Rs.67.50 for 30 days as gas bill. If it uses 35 gas burners for 6 hours a day. Find the amount to be paid if it uses 30 gas burners for 18 days working 7 hours a day.

(A) Rs.40.50

(B) Rs.42.50

(D) Rs.50.50

18. The cost of printing a magazine of 540 pages with 30 lines on each page and 15 words in each line is Rs,7200. Find the cost of printing a magazine of 450 pages with 35 lines on each page and 18 words in each line.

(A) Rs.9000

(B) Rs.9400

(D) Rs.8.400

56. 10 men can do a piece of work in 18 days. In how many days 12 men can do it ?

(A) 12 days

(B) 15 days

(D) 16 days

74. M and N can finish a work in 15 and 20 days respectively. If they do the work together, find the ratio of their income.

(A) 3 : 4

(B) 2 : 3

(D) 3 : 2

75. If 36 bighas of land may be irrigated in 16 days by a well-pump working 15 hours a day. How many days will it take to irrigate 42 bighas of land by the pump working 10 hours a day ?

(A) 30

(B) 28

(D) 32

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42. A sum of money doubles itself in 8 years at some rate of interest. In how many years would it treble itself ?

(A) 16 years .

(B) 12 years

(D) 14 years

43. A sum of amounts will be doubled in 71/2 years. What is the rate percent ?

(A) 152/3

(B) 163/2

(D) 153/2

44. A sum amounts to Rs.1180 in 3 years and to Rs.1300 in 5 years. Find the rate of interest.

(A) 5%

(B) 6%

(D) 8%

45. A certain sum amounts to Rs.17,200 at 12% simple interest per annum in a period in which Rs.22,080 amounts to Rs.37,536 at 14% simple interest per annum. Find the sum.

(A) Rs.11,250

(B) Rs.12,750

(D) Rs.10,750

46. Ten copies of the book can be bought for a certain sum of money payable at the end of 2 years. 12 copies of the same book can be bought for the same sum in ready cash. What is the rate of interest per annum ?

(A) 12%

(B) 15%

(D) 8%

47. Sita deposited some money in a bank at the rate of simple interest of 5.25% per annum. After 2 years, she has got Rs. 840 as interest. Let us write by calculating, the money she has deposited into the bank.

(A) Rs.8,000

(B) Rs.10,000

(D) Rs.9,000

48. Let us calculate the number of years for which the interest of Rs.600 at the rate of simple interest of 8% per annum will be Rs.168.

(A) 51/2

(B) 41/2

(D) 21/2

49. At the same rate of simple interest per annum, if a principal becomes the amount of Rs.7100 in 7 years and of Rs.6200 in 4 years, let us determine the principal amount.

(A) Rs.4000

(B) Rs.7000

(D) Rs.5000

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50. A weaver cooperative society takes a loan of Rs.15,000 for buying a power loom. After 5 years, the society has to repay Rs.22,125 for recovering the loan. Find the rate of simple interest per annum.

(A) 91/2 % p.a.

(B) 81/2 % p.a.

(D) 61/2 % p.a.

51. If the total interest becomes Rs..x for a principal having the rate of simple interest of x% per annum for x years then, principal will be

(A) Rs. x

(B) Rs.100x

(D) Rs. 100/x2

52. If a principal becomes twice of its amount in 10 years, the rate of simple interest per annum is

(A) 5%

(B) 10%

(D) 20%

53. Calculate the principal whose monthly interest is Rs.1 having the rate of simple interest of 5% per annum.

(A) Rs.300

(B) Rs.120

(D) Rs.480

54. Write the number of years in which the amount becomes twice of the principal having the rate of simple interest 61/4 % per annum.

(A) 15

(B) 12

(D) 16

55. The ratio of the principal and the amount (principal along with interest) in 1 year is 8 : 9, the rate of simple interest per annum is

(A) 111/2 %

(B) 121/2 %

(D) 131/2 %

57. Present price of a machine in Rs.2p and if price of the machine decreases by 2r% in each year, the price of machine after 2n years will be

(A) Rs. p(1−r/100)n

(B) Rs. 2p(1−r/50)n

(D) Rs. 2p(1−r/50)2n

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58. A person deposited Rs.100 in a bank and got the amount Rs.121 for two years, the rate of compound interest per annum is

(A) 10%

(B) 20%

(D) 101/2%

59. Find the rate of compound interest per annum, so that the amount on Rs.400 for 2 years becomes Rs.441.

(A) 6

(B) 7

(D) 9

60. If a sum of money doubles itself at the fixed rate of compound interest per annum in n years, find in how many years it will become four times.

(A) 3n

(B) n2

(D) 3n2

61. Determine the principal amount that at the rate of 5% compound interest per annum becomes Rs.615 after two years.

(A) Rs.6000

(B) Rs.8000

(D) Rs.9000

62. If the rate of increase in population is r% per year, the population after n years is p : let us find the population that was n years before.

(A) p(1+r/100)n

(B) p(1+r/100)2n

(D) p(1+r/100)-2n

19. If a, b, c and x be the 1st, 2nd, 3rd and the 4th proportions respectively, then the value of x will be one of the following :

(A) ab/c

(B) ac/b

(D) ab/c

20. The number √7

(A) lies between 1 and 2

(B) lies between 2 and 3

(D) lies between 6 and 7

21. 300 – √45 + √125 – √108 – √20 – √48 =?

(A) 5

(B) 0

(D) 3

92. 3√3 – 4(√7+√3) + √112 + √3 = ?

(A) 5

(B) 3

(D) 0

93. What least number must be added to 8275 to make the sum a perfect square ?

(A) 4

(B) 8

(D) 6

94. What least number must subtracted from 732 to make the remainder a perfect square ?

(A) 3

(B) 4

(D) 6

95. By what number must 192 be multiplied, so that the product may be a perfect square ?

(A) 5

(B) 4

(D) 2

96. By what least number must 1260 be divided to make the quotient a perfect square ?

(A) 35

(B) 30

(D) 45

97. The boys of a school can be arranged in 15, 18 or 24 equal rows and also into a solid square. Find the least number of boys in the school.

(A) 3800

(B) 4000

(D) 1000

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WBCS Main Question Paper – 2018

1. The ratio of Velocity of hour’s hand and minute’s hand at a clock is

(A) 1 : 12

(B) 12 : 1

(D) 24 : 1

36. In an examination it is required to get 310 at the aggregate marks to pass. A student gets 28% mark and is declared failed by 93 marks. What are the maximum aggregate marks a student can get ?

(A) 685

(B) 765

(D) 875

41. A man bought a house for Rs.5 lakhs and rents it. He puts 121/2% of each month’s rent aside for repairs, pays Rs.1660 as annual taxes and realises 10% on his investment thereafter. The monthly rent of the house is

(A) Rs. 2460

(B) Rs. 2500

(D) Rs.5000

42. A trader mixes three varieties of groundnuts costing Rs. 50, Rs. 20 and Rs. 30 per kg. in the ratio 2 : 4 : 3 in terms of weight and sells the mixture at Rs. 33 per kg. What percentage of profit does he make ?

(A) 8%

(B) 9%

(D) None of the above

43. Which of the following ratios is greatest ?

(A) 7 : 15
(B) 15 : 23

(D) 21 : 29

44. If the edge of a cube is increased by 25% then percentage increase in its surface area is (x + y + xy/100 )

(A) 25%

(B) 48.75%

(D) 56.25%

47. Average of ten positive numbers is x¯. If each number is increased by 10%, then x¯

(A) remains unchanged.

(B) may decrease.

(D) is increased by 10%.

57. A plot of 640 sq.ft. is available at the rate of Rs. 4,600 per sq.ft. If 30% of the total cost of the plot is to be paid for booking the plot. How much is the booking amount ?

(A) Rs.9,38,100

(B) Rs.8,83,200

(D) Rs.8,38,100

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64. Sushant spent 18% of his monthly salary on buying electronic goods and 32% of the monthly salary on repair work in his house. Out of remaining amount he invested 42% in fixed deposit. If he was left with Rs. 12,325, how much is his annual salary ?

(A) Rs. 5,18,000

(B) Rs. 5,15,600

(D) Rs. 5,01,000

65. Present age of Neha and Rashmi are in the ratio of 7 : 8 respectively. Six years hence, the ratio of their ages will become 9 : 10 respectively. What is Rashmi’s present age ?

(A) 36

(B) 24

(D) 40

94. A survey shows that 73% of the Indians like apples, whereas 65% like oranges. What percentage of Indians like both apples and oranges ?

(A) 83%

(B) 8%

(D) 35%

95. A man saved Rs. 16,500 in 10 years. In each year after the first year he saved Rs. 100 more than he did in the preceding year. How much did he save in the first year ?

(A) Rs.1200

(B) Rs.1650

(D) Rs.1020

Babu have made 4% loss by selling 12 toffees at Rs.5. How many toffees he would sell at Rs. 10 to get 28% profit ?

(A) 28

(B) 18

(D) 9

A boy recorded the weight of some of his friends as 32kg, 30kg, 40kg, 65kg, 54kg, 38kg, 36kg, 45kg, 50kg, 52kg, 40kg. What is the median ?

(A) 38 kg

(B) 40 kg

(D) 43.8 kg

The number of coconuts plucked from each tree is 1 more than the number of coconut trees in Anil’s garden. The total number of coconut plucked is 132. The total number of coconut trees in the garden is

(A) 12

(B) 22

(C) 11

(D) 33

It has been seen in a survey of a region that 70 persons read English newspaper, 73 persons read Bengali newspaper and 64 persons read both the papers. If 63 persons do not read any paper on how many people the survey has been done ?

(A) 79

(B) 142

(D) 143

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Total expenses of a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders are 120 and 100 the total expenses are Rs. 2000 and Rs.1700 respectively. Find the total number of boarders if the total expense is Rs. 1880.

(A) 200

(B) 112

(D) 115

The sum of three consecutive multiples of 3 is 72. What is the largest number ?

(A) 21

(B) 24

(C) 27

(D) 36

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantities sold at 18% profit is

(A) 400 kg

(B) 560 kg

(C) 600 kg

(D) 640 kg

If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percentage is

(A) 25%

(B) 331/3%

(C) 50%

(D) 66 2/3%

A cricket team won 3 matches more than they lost. If a Win gives them 2 points and Loss (-1) point, how many matches, in all, have they played if their score is 23 ?

(A) 17

(B) 20

(C) 37

(D) 40

Free books were distributed equally among children of a class. The number of books each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 books. How many books were distributed in total ?

(A) 256

(B) 432

(C) 512

(D) 640

If an amount of Rs.84,105 is distributed equally amongst 35 children. How much amount would each child get ?

(A) Rs.2,430

(B) Rs.2,043

(C) Rs.2,403

(D) None of the above

Total price of 6 shirts and 7 trousers is Rs.4,130 while that of 4 shirts and 9 trousers is Rs.4,270. Find out the price of 3 shirts.

(A) Rs.850

(B) Rs.840

(D) Rs.810

Rohan appeared for the Global Talent Search Examination wherein 4 marks are awarded for every correct answer and 1 mark is deducted for every wrong answer. Rohan attempted all the 60 questions and secured 130 marks. What would have been his score if there was no negative marking ?

(A) 140

(B) 152

(D) 168

It costs Rupee 1 to photocopy a sheet of paper. However 2% discount is allowed on all photocopies done after first 1000 sheets. The discount increases to 5% for all photocopies exceeding 2500 sheets. How much will it cost to copy 5000 sheets of paper ?

(A) Rs.4845

(B) Rs. 4870

(D) None of the above

Amal and Bimal started a business. Amal invested Rs. 500 for 9 months and Bimal invested some money for 6 months. If they make a profit of Rs. 69 in a year and Bimal gets profit share of Rs. 46. The capital of Bimal in the business is

(A) Rs. 1500

(B) Rs. 3000

(D) Rs. 6000

A, B and C entered into a partnership business by investing Rs.64000, Rs.52000 and Rs.36000 respectively for a certain period of time. If A receives Rs.35584 as annual profit, what amount will C receive as his share in the profit ?

(A) Rs. 20016

(B) Rs. 20632

(D) Rs. 21084

58. A single person takes 6 minutes to fill a bottle. If from 11 am to 12.30 pm 1845 bottles are to be filled, how many persons should be employed on this job ?

(A) 121

(B) 127

(D) 139

66. A is twice as good a workman as B. A and B together complete a piece of work in 28 days. In how many days will A alone do the same piece of work ?

(A) 40 days

(B) 42 days

(D) 36 days

85. A contractor employed 100 labours, both male and female. Each female labourer receives Rs.144 as daily wages while each male labourer receives Rs.96 as daily wages. If the contractor distributes Rs.12,480 daily as wages, how many more female labourers did he employ than male labourers ?

(A) 20

(B) 25

(D) 35

67. A boat man can row a boat downstream and upstream at 13 kmph and 9 kmph respectively. What will be the speed of boat in still water ? (in kmph)

(A) 12

(B) 10.5

(D) 10

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69. If a man runs 6 kmph from his house, he misses the train at the station by 8 minutes. If he runs at 10 kmph, he reaches the station 7 minutes earlier then the departure of the train. What is the distance of the station from his house ? (in km.)

(A) 43/4

(B) 31/2

(D) 33/4

13. A small owner took a loan of Rs.73000 from his friend. He repay principal along with interest Rs.73100 after 1 day. The rate of simple interest per annum is

(A) 10%

(B) 0.5%

(D) 50%

21. Through the publicity of road safety programmes the street accident in a state has been decreased by 10% in comparison to its previous year. In the present year if the number of street accidents be 2187, the number of street accidents that had been in the state 3 years before is

(A) 4000

(B) 2430

(D) 1458

38. How much time will it take for an amount of Rs.450 to yield Rs.81 as interest at 4.5% per annum of simple interest ?

(A) 3.5 years

(B) 4 years

(D) 5 years

39. The compound interest on Rs.30000 at 7% per annum is Rs.4347. The period (in years) is

(A) 2

(B) 21/2

(D) 4

40. What is the difference between the compound interests on Rs.5000 for 11/2 years at 4% per annum compounded yearly and half-yearly ?

(A) Rs. 2.04

(B) Rs. 3.06

(D) Rs. 8.30

51. If the total interest becomes Rs.x for any principal having the rate of simple interest of x% per annum for x years then the principal will be

(A) Rs. x

(B) Rs. 100x

(D) Rs. 100/x2

78. Ankur invested a sum of Rs.16,800 for four years in a scheme. The rate of interest in the scheme is 8% per annum compounded yearly for the first two years and 10% for the 3rd and 4th years compounded yearly. What will be the compound interest at the end of 4 years ?

(A) Rs. 6810

(B) Rs. 6910

(D) Rs. 6210

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98. Present price of a machine is Rs. p and if price of the machine increases by 2r% in each year, the price of machine will be after n year —

(A) P(1 + r/100)n

(B) P(1 + r/50)n

(D) P(1 – r/100)n

99. Ramen deposits Rs.100 on the first day of every month in a monthly savings scheme. In this way, he has deposited money for 1 year. If the rate of simple interest is 6% per annum; then the amount he will get at the end of the year is

(A) Rs. 1236

(B) Rs. 1239

(D) Rs. 1260

If = X / 2Y = 6 / 7, the value of X – Y / X + Y + 14 / 19 is

(A) 13 / 19

(B) 15 / 19

(C) 1

(D) 1 1 / 19

The sum of all two digit numbers divisible by 5 is

(A) 1035

(B) 1245

(D) 945

The number 0 is

(A) whole number but not integer.

(B) integer but not rational.

(D) whole number, integer, rational and real number.

πand 22 / 7 are

(A) both are rational number.

(B) both are always irrational number.

(D) π is irrational and 22/7 is rational.

The value of (0.243)0.2x (10)0.6is

(A) 0.3

(B) 3

(D) 9

What is the smallest number to be subtracted from 549162 in order to make it a perfect square ?

(A) 28

(B) 36

(D) 81

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If the number 97251*6 is completely divisible by 11, then the smallest whole number in place of * will be

(A) 6

(B) 2

(D) 5

Ram was asked to find 7/8 of a fraction but he mistakenly divided the fraction by 7/8. As a result the difference between the answers was 75/784 . What should be the Ram’s correct answer ?

(A) 13/32

(B) 9/14

(C) 5/16

(D) 5/14

√324 + √1296 equal to

(A) 52

(B) 44

(C) 54

(D) 42

The square of a number is 48 more than 22 times of itself. Find the number.

(A) 25

(B) 22

(C) 24

(D) 28

What will come in place of question mark ?

12, 18, 36, 90, 270, ?

(A) 945

(B) 960

(D) None of the above

If the product of two successive positive integers is 7482. which is the greatest integer ?

(A) 87

(B) 82

(D) 89

35% of 200 + √x = 48% of 550 – 10% of 150. Then x equal to

(A) 600

(B) 21

(C) (179)2

(D) 35721

123456789 x 8 + 9 is equal to

(A) 98765431

(B) 89765431

(C) 987654321

(D) None of the above

If C = temperature in centigrade thermometer F = temperature in Fahrenheit thermometer and they are related by C/5 = (F−32) / 9, then find the temperature whose value is same in both thermometer.

(A) – 42

(B) – 40

(D) 42

If 1.00029 = L( 1 + 2.9 × 10-5 × 10 ), the value of L is

(A) 0.001

(B) 1

(D) 10-2

If -7 ≤ x ≤ 7 and 0 ≤ y ≤ 12, what is the greatest possible value of (y – x) ?

(A) -19

(B) 5

(D) 19

11111 x 11111 is equal to

(A) 111111111

(B) 123454321

(D) 14325321

The product of two numbers is 1320 and their H.C.F. is 6. The L.C.M. of number is

(A) 220

(B) 1314

(D) 7920

102 + 1/100 + 0.0001 equals to

(A) 1.000101

(B) 10.00101

(C) 100.0101

(D) None of the above

If S = ut + 1/2 at2 and u = 50, a = 9.8, t = 2 the value of S is

(A) 119.6

(B) 109.8

(D) 139.2

4 + 0.4 + 0.04 + 0.004 – 0.23 = ?

(A) 4.226

(B) 4.224

(D) 4.214

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For her parents’ 50th wedding anniversary celebration Malina decides to buy 50 balloons. Her supplier only sells balloons in bunches of 12 for Rs, 250 and 7 for Rs. 175. Malina buys exactly 50 balloons. What is the total price she pays ?

(A) Rs.1042

(B) Rs.1100

(D) Rs.1225

There are five positive observations. Average of the first three observations is 8 and that of the last three observations is 6. If the average of all five observations is 6, what is the third observation ?

(A) 10

(B) 8

(C) 12

(D) 14

The value of √0.4¯ is

(A) 0.6¯

(B) 0.7¯

(D) 0.9¯

17. If we subtract √5 from √125, the value is

(A) √80

(B) √120

(D) None of the above

27. The sum of digits of a two-digit number is 12. When the digits are interchanged, the resulting number is 36 more than original number. What is the original two-digit number ?

(A) 93

(B) 48

(D) 84

29. 1 nanosecond is equal to

(A) 10-6 second

(B) 10-9 second

(D) 10-3 second

34. 0.04 x X = 0.000016, X = ?

(A) 0.0004

(B) 0.04

(D) None of the above

46. When the numerator of a fraction increases by 4, the fraction increases by 2/3 . The denominator of the fraction is

(A) 2

(B) 3

(D) 6

88. At the ‘Shoot and Win’ stall in a fair, X fires 5 shots to Y’s 3 but X hits the target only once in three shots while Y hits once in 2 shots. When Y has missed 27 times, X has hit his target ?

(A) 30 times

(B) 60 times

(D) 90 times

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WBCS Main Math paper

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