UPSC question paper – 2016-2020 – ARITHMETIC



UPSC previous year question paper of subject ARITHMETIC from the year 2016 to 2020 with answers



#1. What is the largest number among the following? [2020-]

#2. A shop owner offers the following discount options on an article to a customer: [2020-II] 1. Successive discounts of 10% and 20%, and then pay a service tax of 10%. 2. Successive discounts of 20% and 10%, and then pay a service tax of 10%. 3. Pay a service tax of 10% first, then successive discounts of 20% and 10%. Which one of the following is correct?

#3. In a class, there are three groups, A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight for the students of the class? [2020]

#4. For what value of n, the sum of digits in the number (10n + 1) is 2? [2020]

#5. A sum of `2,500 is distributed among X, Y and Z in the ratio 135 : : 246 . What is the difference between the maximum share and the minimum share? [2020]

#6. What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100? [2020]

#7. What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case? [2020]

#8. The recurring decimal representation 1.272727 ... is equivalent to [2020]

#9. As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for `1,200. What was the original price of rice per kg. [2020]

#10. A bottle contains 20 litres of liquid A., 4 litrs of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture? [2020]

#11. A frog tries to come out of a dried well 4.5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well? [2020]

#12. A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4? [2020]

#13. Let p, q, r and s be natural numbers such that [2020-] p – 2016 = q + 2017 = r – 2018 = s + 2019 Which one of the following is the largest natural number?

#14. How many pairs of natural numbers are there such that the difference of whose squares is 63? [2020]

#15. Let XYZ be a three-digit number, where (X+ Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by [2020]

#16. How many zeroes are there at the end of the following product? [2020] 1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60

#17. Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D? [2020]

#18. A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence? [2020]

#19. If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure? [2020]

#20. In the sum [2020] Ä + 1 Ä + 5 Ä + Ä Ä + Ä 1 = 1 Ä Ä for which digit does the symbol Ä stand?

#21. Two Statements S1 and S2 are given below with regard to two numbers followed by a Question: [2020] S1: Their product is 21. S2: Their sum is 10. Question: What are the two numbers? Which one the following is correct in respect of the above Statements and the Question?

#22. Two Statements S1 and S2 are given below followed by a Question: [2020] S1: n is a prime number. S2: n leaves a remainder of 1 when divided by 4. Question: If n is a unique natural number between 10 and 20, then what is n? Which one of the following is correct in respect of the above Statements and the Question?

#23. A person bought a car and sold it for ` 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car? [2020]

#24. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4? [2020]

#25. Two Statements are given followed by two Conclusions: Statements: [2020] All numbers are divisible by 2. All numbers are divisible by 3. Conclusion-I: All numbers are divisible by 6. Conclusion-II: All numbers are divisible by 4. Which of the above Conclusions logically follows/follow from the two given Statements?

#26. The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are [2019]

#27. Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered? [201915%15%15%]

#28. Ena was born 4 years after her parents, marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena’s father get married? [2019-]

#29. If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?[2019]

#30. In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored? [2019]

#31. The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7.The number of such pairs is [2019]

#32. All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data? [2019] 1. 40% members went for shopping as well as sightseeing. 2. 20% members went for only shopping. Select the correct answer using the code given below :

#33. In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct? [2019] 1. At least 30 Indian participants are vagetarian. 2. At least 10 Indian participants are non-vegetarian. Select the correct answer using the codes given below :

#34. Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent `1300 and Rajesh spent `1500. If each racket costs three times a ball does, then what is the price of a racket ? [2019]

#35. In 2002, Meenu’s age was one-third of the age of Meera, whereas in 2010, Meenu’s age was half the age of Meera. What is Meenu’s year of birth? [2019]

#36. Raju has ` 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows ` 2000 from a friend. Then [2019]

#37. In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football? [2019]

#38. A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A? [2019]

#39. The number of times the digit 5 will appear while writing the integers from 1 to 1000 is [2019]

#40. Number 136 is added to 5B7 and the sum obtained is 7A3, where A and B are integers. It is given that 7A3 is exactly divisible by 3. [2019]The only possible value of B is

#41. A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother? [2019]

#42. In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is [2019]

#43. A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time? [2019]

#44. An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible? [2019]

#45. Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is [2019]

#46. X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?[2018]

#47. If X is between – 3 and – 1, and yis between – 1 and 1, then 4 4 X Y- is in between which of the following?[2018]

#48. 19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform? [2018]

#49. A student has to get 40% marks to pass in an examination. Suppose he gets 30 marks and fails by 30 marks, then what are the maximum marks in the examination? [2018-]

#50. A bookseller sold ‘a’ number of Geography textbooks at the rate of ` x per book, ’a + 2’ number of History textbooks at the rate of ` (x + 2) per book and ‘a – 2’ number of mathematics textbooks at the rate of ` (x –2) per book. What is his total sale in `? [2018]

#51. A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first number itself by 198, then the difference between the first and last digits is [2018]

#52. There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices? [2018]

#53. If x – y = 8, then which of the following must be true? 1. Both x and y must be positive for any value of x and y. 2. If x is positive, y must be negative for any value of x and y. 3. If x is negative, y must be positive for any value of x and y. Select the correct answer using the code given below. [2018]

#54. A person bought a refrigerater worth ` 22,800 with 12.5% interest compounded yearly. At the end of first year he paid ` 8,650 and at the end of second year ` 9,125. How much will he have to pay at the end of third year to clear the debt? [2018]

#55. A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults? [2018]

#56. Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling? [2017]

#57. The monthly incomes of X and Y are in the ratio of 4 : 3 and their monthly expenses are in the ratio of 3 : 2. However, each saves ` 6,000 per month. What is their total monthly income? [2017]

#58. A 2-digit number is reversed. The larger of the two numbers is divided by the smaller one. What is the largest possible remainder [2017]

#59. There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?[2017]

#60. P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?[2017]

#61. The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again? [2017]

#62. If for a sample data [2017-II] Mean < Median < Mode then the distribution is[2017]

#63. How many numbers are there between 99 and 1000 such that the digit 8 occupies the units place? [2017-]

#64. Certain 3-digit numbers have the following characteristics: 1. All the three digits are different. [2017] 2. The number is divisible by 7. 3. The number on reversing the digits is also divisible by 7. How many such 3-digit numbers are there?

#65. There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?[2017]

#66. There is a milk sample with 50% water in it. If 1/3rd of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to [2017]

#67. There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first five such numbers, then what is the mean of all the thirteen numbers? [2017]

#68. A clock strikes once at 1o'clock, twice at 2o'clock and thrice at 3 o'clock, and so on. If it takes 12 seconds to strike at 5 o'clock, what is the time taken by it to strike at 10 o'clock?[2017]

#69. In a city, 12% of households earn less than ` 30,000 per year, 6% households earn more than ` 2,00,000 per year, 22% households earn more than `1,00,000 per year and 990 house- holds earn between ` 30,000 and ` 1,00,000 per year. How many households earn between ` 1,00,000 and ` 2,00,000 per year? [2017]

#70. A watch loses 2 minutes in every 24 hours. while another watch gains 2 minutes in every 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24-hour clock is followed?[2017]

#71. Suppose the average weight of 9 persons is 50 kg. The average weight of the first 5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg, Then the weight of the 5th person will be [2017]

#72. Gopal bought a cell phone and sold it to Ram at 10% profit. Then Ram wanted to sell it back to Gopal at 10% loss. What will be Gopal's position if he agreed? [2017]

#73. There are three pillars, X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance. A climbs on X by 6cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of the requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?

#74. If there is a policy that 1 / 3rd of a population of a community has migrated every year from one place to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period? [2017]

#75. What is the total number of digits printed, if a book containing 150 pages is to be numebred from 1 to 150 [2017]]

#76. Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X ?[2016]

#77. The monthly average salary paid to all the employees of a company was ` 5000. The monthly average salary paid to male and female employees was ` 5200 and ` 4200 respectively. Then the percentage of males employed in the company is:[2016]

#78. In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?[2016]

#79. Anita’s mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is:[2016]

#80. In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of ` 2 by one student only, the total collection is ` 443. Then how many students are there in the class?[2016]

#81. 30g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar Was mixed in 280 ml of water in vessel B and 20 g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is[2016]

#82. A class starts at 11:00 am and lasts till 2:27 pm. Four periods of equal duration are held during this interval. After every period, a rest of 5 minutes is given to the students. The exact duration of each period is:[2016]

#83. A person allows 10% discount for cash payment from the marked price of a toy and still he makes a 10% gain. What is the cost price of the toy which is marked ` 770? [2016]

#84. A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability, that the arrows fall in the red region of the archery target?[2016]

#85. In a race, a competitor has to collect 6 apples which are kept in a straight line on a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is 5 meters from the first apple and all other apples are placed 3 meters apart? [2016]

#86. The average monthly income of a person in a certain family of 5 is ` 10,000. What will be the average monthly income of a person in the same family if the income of one person increased by ` 1,20,000 per year?[2016]

#87. W can do 25% of a work-in 30 days, X can do 1/4 of the work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first? [2016]

#88. How many numbers are there between 100 and 300 which either begin with or end with 2?[2016]

#89. If R and S are different integers both divisible by 5, then which of the following is not necessarily true? [2016]

#90. Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?[2016]

#91. AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is: [2016]

#92. A person is standing on the first step from the bottom of a ladder. If he has to climb 4 more steps to reach exactly the middle step, how many steps does the ladder have? [2016]

#93. The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is: [2016]

#94. The sum of the ages of 5 members comprising a family, 3 years ago, was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby ?[2016]


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