Ratio & Proportion MCQs for UPSC Prelims

60 practice questions on Ratio & Proportion from the Quantitative Aptitude section of the UPSC Prelims syllabus. 60 come with a written explanation and 34 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

24 Easy 31 Medium 5 Hard 34 from past papers

Sample questions

Q1
Previous year question medium

A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair. While preparing the bill, the bill clerk interchanged the number of black and brown pairs by mistake which increased the bill by 100%. What was the number of pairs of brown socks in the original order?

  1. A 10
  2. B 15
  3. C 20
  4. D 25
Show answer and explanation

Correct answer: D - 25

Let the price of a brown pair be b, so a black pair costs 3b. Let the original number of brown pairs be x. Original bill = 5 black + x brown = 5(3b) + x(b) = 15b + xb. After interchanging the counts, there are x black pairs and 5 brown pairs, so the wrong bill = x(3b) + 5(b) = 3xb + 5b. A 100% increase means the wrong bill is twice the original: 3xb + 5b = 2(15b + xb). Dividing by b: 3x + 5 = 30 + 2x, so x = 25.

Q2
Previous year question medium

Two persons P and Q enter into a business. P puts Rs. 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P's share is Rs. 400 more than Q's share out of the total profit of Rs. 2,000, what is the capital contributed by P?

  1. A Rs. 30,000
  2. B Rs. 26,000
  3. C Rs. 24,000
  4. D Rs. 20,000
Show answer and explanation

Correct answer: A - Rs. 30,000

Out of Rs. 2,000 profit with P getting Rs. 400 more than Q: P's share = 1,200 and Q's share = 800, ratio 3 : 2. Profit shares are proportional to capital x time, so (P x 8) : (Q x 10) = 3 : 2, giving 16P = 30Q, i.e., P = 15Q/8. Also P = Q + 14,000, so 15Q/8 - Q = 14,000, i.e., 7Q/8 = 14,000, giving Q = 16,000 and P = 16,000 + 14,000 = Rs. 30,000.

Q3
Previous year question easy

If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then what is the ratio of the distances travelled by them in one hour?

  1. A 8 : 5
  2. B 5 : 8
  3. C 4 : 5
  4. D 1 : 2
Show answer and explanation

Correct answer: B - 5 : 8

Distance per hour equals speed. Bus speed = 160 / 4 = 40 km/h. Train speed = 320 / 5 = 64 km/h. In one hour the bus covers 40 km and the train covers 64 km, so the ratio is 40 : 64. Dividing both by 8 gives 5 : 8.

Q4
Previous year question medium

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?

  1. A 3 : 1 : 1
  2. B 3 : 2 : 4
  3. C 4 : 3 : 4
  4. D 3 : 1 : 4
Show answer and explanation

Correct answer: A - 3 : 1 : 1

Earnings are shared in proportion to work done, i.e. to the rates of work. Let Q's rate = 1 unit. P works thrice as fast as Q, so P's rate = 3. P and Q together work four times as fast as R: (P + Q) = 4R, so R = (3 + 1)/4 = 1. Thus the rates are P : Q : R = 3 : 1 : 1, which is also the ratio of work done (and hence earnings). Hence (a).

Q5
Previous year question medium

In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speed of A to B assuming that both start at the same time?

  1. A 25 : 21
  2. B 25 : 20
  3. C 5 : 3
  4. D 5 : 7
Show answer and explanation

Correct answer: A - 25 : 21

A runs the full 500 metres to win. B started 45 m ahead, so B needed only 500 - 45 = 455 m to reach the finish line, but B is still 35 m behind the finish when A wins, meaning B has covered 455 - 35 = 420 m in the same time. Since time is equal, the speed ratio equals the distance ratio: A : B = 500 : 420 = 25 : 21. Hence option (a).

Q6
Previous year question easy

A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults?

  1. A 6
  2. B 10
  3. C 12
  4. D 15
Show answer and explanation

Correct answer: B - 10

The full capacity equals 18 adults or 30 children, so the space taken by 18 adults equals that of 30 children. Therefore 1 adult occupies the space of 30/18 = 5/3 children. 12 adults occupy 12 x 5/3 = 20 child-spaces. Remaining capacity = 30 - 20 = 10 children. Answer is 10.

Q7
Previous year question easy

The monthly incomes of Peter and Paul are in the ratio of 4:3. Their expenses are in the ratio of 3:2. If each saves Rs. 6000 at the end of the month, their monthly incomes respectively are (in Rs.) (a) 24000 and 18000 (b) 28000 and 21000 (c) 32000 and 24000 (d) 34000 and 26000

  1. A 24000 and 18000
  2. B 28000 and 21000
  3. C 32000 and 24000
  4. D 34000 and 26000
Show answer and explanation

Correct answer: A - 24000 and 18000

Let incomes be 4x and 3x, and expenses be 3y and 2y. Savings = income minus expense, and each saves 6000: 4x - 3y = 6000 and 3x - 2y = 6000. Multiply the first by 2 and the second by 3: 8x - 6y = 12000 and 9x - 6y = 18000. Subtracting gives x = 6000. So Peter's income = 4x = 24000 and Paul's income = 3x = 18000.

Q8
Previous year question medium

Out of 120 applications for a post, 70 are male and 80 have a driver's license. What is the ratio between the minimum to maximum number of males having a driver's license?

  1. A 1 to 2
  2. B 2 to 3
  3. C 3 to 7
  4. D 5 to 7
Show answer and explanation

Correct answer: C - 3 to 7

There are 120 applicants: 70 male and therefore 50 female. 80 applicants hold a driver's license. To find the minimum number of males with a license, assign licenses to as many females as possible first: all 50 females can hold a license, leaving 80 - 50 = 30 licenses that must go to males. So the minimum number of males with a license is 30. To find the maximum, give licenses to as many males as possible: since there are 70 males and only 80 licenses, all 70 males can hold one. So the maximum is 70. The ratio of minimum to maximum is 30 : 70 = 3 : 7. The official UPSC 2013 key marks (c) 3 to 7, matching the solution.

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More Quantitative Aptitude topics

Number System 188 Permutation, Combination & Probability 94 Percentage 85 Geometry & Mensuration 69 Time, Speed & Distance 66 Algebra 66 Basic Numeracy & Word Problems 66 Clocks & Calendars 56 Sequences & Series 56 Mixtures & Alligation 52 Time & Work 51 Averages 45 Simple & Compound Interest 43 Profit, Loss & Discount 39 Ages 33