Contents
Arithmetic – WBPSC Miscellaneous Main
Separate Answer Books to be used for Group A and Group B
Group B (Arithmetic): 50 Marks
Answers may be written in English or Bengali but all the answers must be in one and the same language
Miscellaneous Main Question – 2019
Answer any ten questions. 5×10=50
- In a club, every member contributed as many 50 rupees as the number of members to raise the subscription amount of Rs.31,250. How many members are there in the club?
- A number becomes 600 if it is reduced by 40%. Find the rate of increase to make it 1600.
- Find the simplest value of √1.2-√0.74-√0.99-√0.85-√0.36
- 50 kgs. of Type-I mixture contains 10 kgs. of urea, while 80 kgs. of Type-II mixture contains 24 kgs. of urea. A total of 60 kgs. of mixture is collected from these two types to prepare a mixture of Type-III and it is found to contain 15 kgs. of urea. What is the ratio of two types of mixtures in the mixture of Type-III?
- 30% of selling price of an article is equal to 40% of its cost price and 45% of its selling price exceeds 50% of its cost price by Rs.10. Determine the cost price of the article.
- Find the rate of increase of the cost price in order to make a profit of 20% by selling an article after giving 10% rebate on marked price to a customer.
- Mixing sand and cement in the ratio 6 : 1, a mason prepared a mixture for construction. At the completion of construction, it is found that yet 70 kgs. of mixture were unused. Then he added more cement to it and prepared a mixture of 5 : 1. How much cement did he add to it later?
- The length of a rectangular field is three times of its breadth and its area is 972 m2. Measure out the perimeter of the field.
- A work is completed 6 days earlier when 60 workers are engaged replacing 40 workers to do it. How many persons are required to complete the same work in 10 days earlier?
- The food of 90 days is stored up for a troop consisting of 500 soldiers. After 18 days, 100 additional soldiers joined the said troop without any additional food. If the amount of money meant for food of each soldier is reduced from Rs.30 to Rs.25, then determine the number of days the food can cater the soldiers.
- There are three pipes fitted in a tank. The first one can fill it in 15 minutes, the second one can fill it in 30 minutes. Only through the third one, the filled in tank becomes empty in 20 minutes. If all the three pipes are opened simultaneously when one-fourth part of the tank is filled up, measure out the amount of time the tank will take to make itself full completely.
- A person gets 5 items more than earlier at the cost of Rs.50 when the cost of it is reduced by Rs.4 per dozen. What is the percentage of reduction of the cost of a dozen of the same items at present?
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Miscellaneous Main Question – 2018
Answer any ten questions. 5×10=50
- The sum of first 15 multiples of 8 is _____.
- Find out the missing term in the series 1, 4, 9, 16, 25, …, 49.
- The difference of two numbers is of their sum and their sum is 45. Find the LCM.
- 9² × ∜(1296) – 254 = (? × 9 + 151)
- In an examination, the average marks obtained by John in English, Maths, Hindi and Drawings were 50. His average marks in Maths, Science, Social Studies and Craft were 70. If the average marks in all seven subjects is 58, his score in Maths was _____.
- In an examination, 20% of total number of Students failed in History, 15% of total number of Students failed in Hindi and 5% of total number of Students failed in both. Find the percentage of Students who passed in both the subjects. Also, find the percentage of Students who failed in either subject.
- If Karan purchases 10 oranges for Rs.25 and sells 9 oranges for Rs.25, find the gain percentage.
- A takes Rs.3,000 from b for 2 years at the rate of 10% half-yearly simple interest. What amount will be paid by A to B after the end of 2 years?
- Two numbers are in the ratio of 2 : 3. If 15 is added to both the numbers, then the ratio between two numbers becomes ¹¹⁄₁₄. Find the greater number.
- A and B together can do a piece of work in 12 days and A alone can do it in 18 days. In how many days can B alone do it?
21. 
- Simplify: (256)¾
- A starts a business with Rs.4,000 and B joins the business 4 months later with an investment of Rs.5,000. After 1 year they earn a profit of Rs.22,000. Find the share of A and B.
- 7 × 0.7 × 0.07 × 7000 = ?
- In a box of marbles, there are three less white marbles than the red ones and five more white marbles than the green ones. If there are a total of 10 white marbles?
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Miscellaneous Question Paper – 2010
Answer any ten questions. 5×10=50
- (a) Write down the greatest and least of the following numbers :
(b) If n be any natural number show that the quantity n3+5n will be divisible by 6.
- The total income of A, B, C is Rs.1665. If they spend 80%, 85% and 75% of their incomes respectively and the ratio of their savings 7 : 6 : 9, what is the income of A?
- A businessman announces that he will sell materials at a profit of 10% on cost price. But the standard weight for 1 kg used by him actually weighs ¹⁵⁄₁₆ kg. What is he actual percentage of profit, he earns?
- In a mixture of three varieties of tea, the ratio of their weights is 4 : 5 : 8. If 5 kg tea of the first variety, 10 kg tea of the second variety and some quantity of tea of the third variety are added to the mixture, the ratio of the weights of varieties of tea in the final mixture.
- A merchant sold each of the two sarees of Rs.96. The profit percent he earned in our saree was as much as the toll percent incurred on another saree. If his total loss by his sale was 4%, determine the percent of the profit or loss.
- What will come in the place of the question mark (?) in the following number series?
1 5 15 34 65 ?
- In order to attract spectators the exhibition authority reduces the per head entrance fee of 25 paise by 20%. As a result daily income of the authority increases by 28% on the sale of tickets. Determine the rate percent of increase in the number of spectators.
- A pump of diameter 6 cm, can fill a reservoir of 4 m long, 3 m broad and 3 m deep with water in 1 hour 15 minutes. What is the breadth of a reservoir of 6 m long and 5 m deep that can be filled by a pump of diameter 7.5 cm, within 1 hour?
- Rs.600 at the rate of 4% simple interest per annum and Rs.500 at the rate of 6% are lent on the same date. After how much time the amounts on both principals be equal?
- A person borrowed Rs.8,000 on a condition that at the end of each year the interest at 10% p.a. will be added with the principal. If he would be free from loan repaying Rs.10,648, how many years later would he repay his loan?
- A can do a piece of work in 20 days and B in 12 days. After doing the work for some days A left and then B began to work in place of A. The work has completed in total 14 days. How many days did A work?
- The distance between two places is 175 km. The time taken by a bus to cover the said distance is 3 hours 45 minutes more than the time taken by a train. The speed of the bus per hour is 15 km, less than that of the train. What is the speed of the bus?
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Miscellaneous Question Paper – 2009
Answer any ten questions. 5×10=50
- (a) If A : B = 2 : 3, B : C = 4 : 7, C : D = 5 : 6 then A : B : C : D = ? 2
(b) Simplify : 3
- The price of a book is marked at Rs.1200. If successive discounts of 20%, 10% and 5% be allowed at what price does customer buy it? 5
- What will come in place of the question mark (?) in the following number series? 5
2 9 28 65
- When the length of a rectangular plot is increased by four times its perimeter becomes 480 meters and area becomes 12,800 sq.m. What was its original length? 5
- A diamond worth Rs.24000 broke into three pieces. If the ratio of the weights of the pieces be 2 : 3 : 5 and if the price of diamond be proportional to the square of its weight, calculate the loss incurred by this breakage. 5
- The rate of interest being increase from 10% to 12½% a man’s yearly income increased by Rs.1250. Find the principal and the increased income. 5
- When a number is divided by 121, the remainder left is 25. Find the remainder when the same number is divided by 11. 5
- Find the compound interest for Rs.2000 for 3 years at the rate of 10% per annum. 5
- A milkman makes 10% profit by selling impure milk for Rs.11.00 per litre. If the cost price of the pure milk is Rs.12 per litre, then find the ratio of pure milk and water in the impure milk. 5
- The average temperature for Monday, Tuesday and Wednesday was 36°C. The average temperature of Tuesday, Wednesday and Thursday was 38°C and that for Thursday was 37°C. What was the temperature on Monday? 5
- A certain distance is covered with a certain speed. If half the distance is covered in double time then find the ratio of the speed to that of the original one. 5
- There is 10% increase in prices. How much consumption should be decreased so that there is no increase in expenditure? 5
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Miscellaneous Question Paper – 2007
Answer any four questions. 4 x 5 = 20
- On a rainy day, 4/15 of the whole strength of a class was absent and ¾ of those present, brought raincoat. How many did not bring raincoat, the total strength of the class being 180?
- Find the least four perfect square number.
- A : B = 2 : 3, B : C = 4 : 7; C : D = 5 : 6. Find the ratio of A to D. Also compare A, B, C, D, i.e. find the continued ratio of A : B : C : D.
- If 80 persons can finish a work within 16 days by labouring 6 hours a day, then how many hours per day should 64 persons work to complete that very job within 15 days?
- There are 240 coins in half rupees, quarter rupees and ten paise of which the values are proportional to 5 : 3 : 1. Find the number of each coin.
- A, B and C enter into partnership. A puts in Rs.800 on 1st January, 1950, B Rs.600 on 1st May and C Rs.500 on 1st July. They make a profit of Rs.348 in all that years. How should the profit be divided?
Section — II
Answer any five questions. 5 x 6 = 30
- A man worked for 4 days, a woman for 6 days and a boy for 5 days to finish certain work and received altogether Rs.66 as their wages. If their daily work be in the proportion of 1/3 : ¼ : 1/6, how much wages should each get?
- Three glasses of equal size have been filled with milk mixed with water. The ratio of milk and water in the first glass is 2 : 3, in the second glass the ratio is 3 : 4 and it is 4 : 5 in the third glass. The milk mixed with water contained in the three glasses is poured into a bottle. What is the ratio of milk and water in the bottle?
- In an examination 35% of the candidates fail in Mathematics and 40% fail in English. If 15% fail in both the subjects, find the percentage of those who pass in both the subjects.
- Starting from a place, a cyclist reaches his destination at a speed of 12 km/hr and returns to the same place at a speed of 8 km/hr. Find the average speed of the whole journey.
- Selling 400 kg of sugar, a shopkeeper make a profit of 4%. Actually he sold some quantity of sugar 2% loss and remaining at 10% profit. Find the quantity of sugar sold at 2% loss.
- A co-operative society for weavers borrowed a sum of money from a Central Co-operative Bank to purchase a weaving machine with the condition that after each period of two years, 1/5 of the sum borrowed along with the interest accrued at 9% rate of simple interest per annum should be paid back. If the money paid back by the society in the first instalment after two years Rs.19000, what is the sum of money borrowed by the society?
- The length of a rectangle was decreased by 5% and the breadth increased by 5%. By what percent did the area of the rectangle change?
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Miscellaneous Question Paper – 2006
Section — I
Answer any six questions. 6 x 5 = 30
- (a) A manufacturer makes 800 articles at a cost of Rs.1.50 per article. He fixes the selling price such that if only 600 articles are sold, he would make a profit of 30% on his outlay. However, he sold 620 articles at this price. Find his actual profit percent of the total outlay, assuming that the unsold articles are useless. 5
(b) A pan contains 200 litres mixture of milk and water in which the quantity of water is 12½% in total. What quantity of water should be added to the said mixture further so as to get the water content of the mixture as 37½%. 5
- (a) A and B started a business jointly. A advanced Rs.5000 and after 4 months gave another Rs. 3000. B advanced Rs.8000 but after 8 months withdrew Rs.2500. If the profit at the end of the year be Rs.5100, find the amount each will get. 5
(b) A and B together can do a piece of work in 12 days while B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C takes up and finishes it alone in 13 days. In how many days could each do the work by himself? 5
- (a) Two pipes can separately fill a tank in 20 hrs and 30 hrs. respectively. Both the pipes are opened to fill the tank but when the tank is ⅓ full, a leak develops in the tank through which ⅓ of the water supplied by both the pipes leak out. What is the total time taken to fill the tank? 5
(b) In an election 75% of the voters cast their votes out of which 2% are rejected. If the successful candidate secures 9261 votes, which is 75% of the total valid votes, determine the total no. of the voters in that centre. 5
- (a) 3 men and 4 boys can earn Rs.756 in 7 days, 11 men and 13 boys can earn Rs. 3008 in 8 days. In what time will 7 men with 9 boys earn Rs.2480? 5
(b) In a mixture of three varieties of tea, the ratio of their weights is 4:5:8. If 5 kg tea of the first variety, 10 kg tea of the second variety and some quantity of tea of the third variety are added to the mixture, the ratio of the weights of three varieties of tea becomes 5:7:9. Find the quantity of the third variety of tea in the final mixture. 5
- (a) Jayantababu borrowed a sum of money from a nationalised bank at 12% simple interest per annum and the same amount at 10% simple interest per annum both for the same period. He cleared the first loan 6 months before the scheduled date of repayment and repaid the second loan just at the end of the scheduled period. If in each case he had to pay Rs.3250 as amount then how much and for what time did he borrow? 5
(b) A train overtakes two persons who are walking in the same direction as the train is moving, at the rate of 2 km/hr and 4 km/hr and passes them completely in 9 and 10 seconds respectively. Find the speed and the length of the train. 5
- (a) The ratio of the land to water for the whole of the Earth is 1:2 and 2 : 3 in the northern hemisphere. Find out the ratio of water to land in the Southern Hemisphere. 5
(b) A man purchases a plot of land for Rs.36000. He sells ⅓ of the land at a loss of 20% and ⅖ of the land at a gain of 25%. At what percent profit or loss must he sell at the remaining land so as to make an overall profit of 10%. 5
- (a) In order to attract more spectators, the exhibition authority reduce the per head entrance fee of 25 paise by 20%. As a result daily income of the authority increases by 28% on the sale of tickets. Determine the rate percent of increase in the number of spectators 5
(b) One aeroplane started 30 minutes later than the scheduled time from a place 1500 km away from its destination. To reach its destination at the scheduled time the pilot had to increase the speed by 250 km/hr. What was the speed of the aeroplane per hour during the journey? 5
Section — II
Answer any two questions. 2 x 10 = 20
- 8 men can finish in 12 days a job for which 12 boys take 16 days. The job has to be finished in 7 days. 16 men start the job and after 3 days, 10 men leave and come many boys join the rest to finish the job in stipulated period. How many boys joined?
- A cloth merchant normally sells his clothes at 10% profit. During a festival sale he puts price labels on clothes in excess by 25% compared to normal sale-price. Then he declares a 15% rebate on his goods. Find the additional amount of gain he makes at the time of festival by selling clothes cost is Rs.1,00,000.
- A cistern is fitted with 3 taps. The first tap fills the cistern while the second and third empty it in equal time. The first tap is kept open for some time so as to fill a part of the cistern and then the second tap is also opened so that the cistern is emptied in 3 hr. If instead of the second, the second and third taps are opened simultaneously, the cistern is emptied in 1 hr. How long was the first tap alone kept open?
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Miscellaneous Question Paper – 2005
Section — I
Answer any six questions. 6 x 5 = 30
- Simplify:
- The ratio of number of 5 rupee denominations, 2 rupee denominations and 1 rupee denominations contained in a box be 3 : 4 : 5 and if their total value be Rs.560, find the number of separate denominations.
- Find the least six digit perfect square number.
- Find the sum of integers greater than 400 and lesser than 500 which is divisible by 12, 16 and 24.
- The ratio of the monthly income of A and B is 5 : 6 and that of their monthly savings is 2 : 3. If their monthly expenditures be Rs.8,000 and Rs.9,000 respectively, find their monthly income.
- If the income of a person decreases by 50%, find the percentage increase of his income so that there is no loss or gain.
- In an examination out of 6,00,000 candidates 5% remain absent. 30% of the appeared candidates failed. The ratio of candidates who passed in first division, in second division and in third division is 2 : 3. Find the number of successful candidates in different divisions.
- There is a census after interval of 10 years starting from 1961. There are increases of population at the rate of 10%, 15% and 40% of a certain city in 1971, 1981 and 1991. If the total population in 1991 be 25,67,950. Find the population of the city in 1961.
Section — II
Answer any two questions. 2 x 10 = 20
- Two retailers A and B purchases one computer each from a whole seller at the rate of Rs.40,000. First retailer A sells the computer at a profit of 20% while the second retailer B enhance the rate by 30% and sells the computer at 8% rebate. Find the profit of each of A and B.
- When water is pumped through a pipe of diameter 6 cm for 25 minutes into a cistern of length 5 metre, breadth 3 metre the height of water raises through 2.4 metre. Find the time required to fill up a cistern of 4 metre length, 3.6 metre breadth and 2 metre height by pumping water through a pipe radius 5 cm.
- A, B and C invest Rs.40,000, Rs.32,000 and Rs.48,000 respectively a bus. They take a loan of Rs.3,00,000 from a bank on that they will pay Rs.60,000 of the principal amount and Rs.10,000 as interest per annum. Of them A works as the driver while B and C work as conductors. From the profit they agree to pay bank dues and ⅓ of the remaining profit they agree to divide in proportion of their individual investments while remaining profit they are to divide in the ratio 3 : 2 : 2. If there be a profit of Rs.1,96,000 in a year; find their shares of profit that year.
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- Solution by smart math Part 2
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Miscellaneous Question Paper – 2004
Answer any five questions
- (a) The sum of two numbers is 256 and their GCM is 32. Find the numbers
(b) Find the prime number(s) if any, between 500 and 520. 5+5
- (a) The circumference of a bicycle wheel is 4 m 8 cm. How many times will it revolve in passing through a distance of 2 km 4 dm?
(b) The price of sugar being raise by 20 per cent. By how much a house holder reduce his consumption of sugar so as to keep his expenditure on it as before? 5+5
- (a) A snail, on the average, creeps 75 cm up a vertical pole during 12 hours in the night, and slips down 40 cm during 12 hours in the day. In what short time will it reach the top of a pole of 5 m 5 cm high?
(b) If 2 men do as much as 5 women and 6 women as much as 10 boys, divide a week’s wages of Rs.7600 among 8 men, 9 women and 15 boys? 5+5
- (a) 75% of total students of a school were boys and the rest girls in March 2002. 75 boys left the school and 75 new girls took admission in the school in April 2003. As a result, the number of girls became 33⅓% of the present students of the school. Find the total number of students in the school.
(b) A glass is full of milk mixed with water in which one-fourth of the mixture is water. How much of it must be taken away and equal quantity of water be poured into the glass so that milk and water will be equal? 5+5
- (a) A person made a fixed deposit of Rs.15,000 in a bank in his locality for 5 years at the simple interest of 10% per annum. He had to withdraw the money but gave a lower rate of interest as money was withdrawn before 5 years have been completed, and he got Rs.3,900 less than what he would have got after 5 years. What was the rate of simple interest paid by the bank?
(b) Six coins of equal weight, made of gold and silver, are melted together and re-cast. In one gold and silver are in the ratio 2 : 3 ; in two others of 3 : 5 ; and in the rest of 5 : 4. In what ration will gold and silver be mixed in the new coin? 5+5
- (a) A man buys a certain number of lemons at 3 for two rupees and equal number at 2 for three rupees. If he sells them at 2 for two rupees. What does he gain or lose per cent?
(b) A cistern is provided with three pipes A, B, C. A and B can fill the empty cistern in 20 minutes and 30 minutes respectively, while C can empty it in 15 minutes. If A, B and C kept open in succession for one minute how soon will the cistern be filled? 5+5
- (a) The distance between two cities is 300 km. Two trains one Express and other Passenger, run form one another. The average speed of the Express train is 10 km per hour more than that of the Passenger train, and the express train takes 90 minutes less time than that for the Passenger train for the whole journey. Find the average speed of the Passenger train.
(b) A dishonest tradesman marks his goods at the advance of 5 p.c. on the cost price and also uses a fraud weight balance whose beam is horizontal when the weight on one scale is one-fifteenth more than the weight on the trader. What is his actual gain per cent? 5+5
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Miscellaneous Question Paper – 2003
Section — I
Answer any six questions. 6 x 5 = 30
- 42 litres of adulterated milk contain milk and water in the ratio 4 : 3. What amount of water must be added to it so that the resulting mixture may contain milk and water in the ratio 4 : 5?
- A piece of cloth is sold for Rs.85.80 at a profit would have been Rs.16.50. Find the length of the piece.
- A man after paying an income tax 6p in a rupee, has Rs.4794 left. Find out his gross income.
- A man has deposited Rs.2,500 in a bank in 1st January and withdraws Rs.1,000 from the bank at the end of 9 months. If the rate of interest is 4% p.a., then find the total interest payable to him at the end of the year.
- 20 men working 8 hours a day can complete a work in 18 days. In how many days 16 men working 9 hours a day can complete this works?
- Of the four members (p,q,r,s) the ratio of the first number to the second is (2 : 3), that of the second to the third is (5 : 6) and that of the third and the fourth is (8 : 9). What is the continued ratio of the four members?
- The sum of the present ages of the father and son is 56 years. After seven years the ratio of their ages will be (5 : 2). Find the present age of son.
- A broker sells two cars at Rs.39100 each. He gains 15% on one car and loses 7.5% on the other. What is his total profit in the transaction?
- Two pipes can fill a cistern in 20 and 30 minutes respectively. Both the pipes are opened, when must the first pipe be turned off so that the cistern may be filled in 10 minutes more?
Section — II
Answer any two questions. 2 x 10 = 20
- A foot path of uniform width runs round the inside edge of a rectangular field 38 m long and 32 m wide. If the area of the path is 600 sq.m., find the width of the path.
- In an examination 35% students fail in Mathematics and 30% fail in English. 20% of the students failed in both subjects; find the total number of students.
- A man walking uniformly at a speed of 2 km/hr, he would reach 5 minutes earlier. What is the exact period of journey for him to reach the office?
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Miscellaneous Question Paper – 2002
Section — I
Answer any six questions. 6 x 5 = 30
- Find the two numbers whose L.C.M. is 420 and sum is 144.
- Establish with reasons that 947 is a prime number.
- If the price of pins be diminished by 2 paisa per dozen, 6 more pins are available in 42 paisa. Find the present price of pins per dozen.
- A person takes some loan from a bank at 10% simple interest for five years. He realises that he would have got a larger amount of loan for the same amount of interest for six years if he took the loan from a Co-operative bank giving loan would have been ⁷/₁₈th of the loan from bank.
- In a school 35 students play tennis, 30 students play football and ten students play only cricket. If total number of students is 100 and 45 students play no games. Find the number of students
(i) Playing tennis only
(ii) Playing both tennis and football
- A train leaves Howrah at 7 a.m. and reaches Burdwan at 11 a.m. Another train leaves Burdwan at 8 a.m. and reaches Howrah at 10:30 a.m. Find the times the trains take to reach their destinations after crossing each other.
- Two taps A and B can fill a cistern in 20 and 30 minutes respectively and Tap C can empty it in 40 minutes. The cistern is half full of water and the three taps are kept open for 2 minutes. The Tap B is then kept closed for another 4 minutes. It is found that only 17 litres of water can now fill the cistern. Find how much water were there in the cistern at the beginning.
- A boat takes 4 hours more time in going down the stream 28 km, and up the stream through same distance, than the time for journey down-stream and up-stream both 24 km. If velocity of boat is 3 times that of stream, find the velocity of stream.
Section — II
Answer any two questions. 2 x 10 = 20
- Allowing a discount of 10% on market price a trader gains 5% on an article. If he increases the marked price by 10% and then allows a discount of 15% show that his gain exceeds 9%.
- In two jars there are mixtures of milk and water in the ratios 3 : 4 and 4 : 5. Mixtures are taken from the two jars in the ratio 1 : 3 respectively and are poured into a third jar. Find the ratio of milk and water in the third jar. When 20 litres of milk are added to the third jar the ratio of milk and water there becomes 1 : 1. How much mixture was taken from the second jar?
- A man gets over and above his monthly salary, a house rent of Rs.80.00 and dearness allowance of Rs.120.00 each month. Of his annual income, RS.5000.00 is tax-free but on next Rs.5000.00 the tax is 10%. The remaining part of income is taxable at 15%. His yearly insurance premium of Rs.1200.00 is also tax-free. If he pays an early tax of Rs.980.00 find his monthly income.