Basic Numeracy & Word Problems MCQs for UPSC Prelims

66 practice questions on Basic Numeracy & Word Problems from the Quantitative Aptitude section of the UPSC Prelims syllabus. 66 come with a written explanation and 52 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

34 Easy 29 Medium 3 Hard 52 from past papers

Sample questions

Q1
Previous year question medium

The 5-digit number PQRST (all distinct digits) is such that T is not 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?

  1. A 3
  2. B 4
  3. C 5
  4. D 6
Show answer and explanation

Correct answer: B - 4

Conditions: P = 3T with T not 0, S = Q + 4 and Q = R + 3 (so S = R + 7), and all five digits distinct. P = 3T allows only T = 1 (P = 3), T = 2 (P = 6) or T = 3 (P = 9). S = R + 7 with S a digit allows only R = 0, 1 or 2, giving (R, Q, S) = (0, 3, 7), (1, 4, 8) or (2, 5, 9). Now combine and reject clashes. T = 1, P = 3: (0, 3, 7) clashes with P = 3; (1, 4, 8) clashes with T = 1; (2, 5, 9) works, giving 35291. T = 2, P = 6: (0, 3, 7) works, giving 63072; (1, 4, 8) works, giving 64182; (2, 5, 9) clashes with T = 2. T = 3, P = 9: (0, 3, 7) clashes with T = 3; (1, 4, 8) works, giving 94183; (2, 5, 9) clashes with P = 9. Valid numbers: 35291, 63072, 64182, 94183, a total of 4. The official UPSC key confirms option (b).

Q2
Previous year question medium

Four persons, Alok, Bhupesh, Chander and Dinesh have a total of Rs. 100 among themselves. Alok and Bhupesh between them have as much money as Chander and Dinesh between them, but Alok has more money than Bhupesh; and Chander has only half the money that Dinesh has. Alok has in fact Rs. 5 more than Dinesh has. Who has the maximum amount of money?

  1. A Alok
  2. B Bhupesh
  3. C Chander
  4. D Dinesh
Show answer and explanation

Correct answer: A - Alok

Alok plus Bhupesh equals Chander plus Dinesh, and together they total 100, so each pair holds 50. Chander has half of Dinesh, so Chander plus Dinesh equals 1.5 times Dinesh equals 50, giving Dinesh = 33.33 and Chander = 16.67. Alok is 5 more than Dinesh, so Alok = 38.33, and Bhupesh = 50 - 38.33 = 11.67. The largest share belongs to Alok.

Q3
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.

Q4
Previous year question medium

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:

  1. A 1
  2. B 5
  3. C 7
  4. D 9
Show answer and explanation

Correct answer: B - 5

Correct answers: arithmetic = 70% of 10 = 7, algebra = 40% of 30 = 12, geometry = 60% of 30 = 18. Total correct = 7 + 12 + 18 = 37. To pass she needs 60% of 70 = 42 correct. Shortfall = 42 - 37 = 5. So she needs 5 more correct answers. The other options do not match the required 42 minimum.

Q5
Previous year question medium

A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for

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

Correct answer: B - 3 days

Tank volume = 20 x 15 x 6 = 1800 cubic metres. Since 1 cubic metre = 1000 litres, the tank holds 1800 x 1000 = 18,00,000 litres. Daily requirement = 4000 people x 150 litres = 6,00,000 litres per day. Number of days the water lasts = 18,00,000 / 6,00,000 = 3 days.

Q6
Previous year question easy

P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score?

  1. A 360
  2. B 380
  3. C 400
  4. D 420
Show answer and explanation

Correct answer: A - 360

Let Q's score be q, so P's score is q + 40. Q scored 10% less than P, so q = 0.9 (q + 40), giving q = 0.9q + 36, hence 0.1q = 36 and q = 360 - option (a). Quick check: P = 400 and 10% less than 400 is 360, consistent. Option (c) 400 is P's score, not Q's. Options (b) 380 and (d) 420 satisfy neither the 40-mark gap nor the 10% relation simultaneously.

Q7
Previous year question medium

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?

  1. A 28
  2. B 29
  3. C 30
  4. D 31
Show answer and explanation

Correct answer: B - 29

The well is 4.5 m = 450 cm deep. In each jump-and-slide cycle the net gain is 30 - 15 = 15 cm, but on the final jump the frog escapes and does not slide back. On the last successful jump the frog rises 30 cm and is out, so it must reach a height of 450 - 30 = 420 cm by net progress before that final jump. To gain 420 cm at 15 cm net per jump takes 420 / 15 = 28 jumps. The 29th jump then carries it from 420 cm up 30 cm to 450 cm, clearing the well. Total jumps = 29.

Q8
Previous year question easy

A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?

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

Correct answer: A - 10 kg

Let the empty vessel weigh E and a full load of water weigh W. Full: E + W = 40. One-third filled: E + W/3 = 20. Subtract the second from the first: W - W/3 = 40 - 20, so (2/3)W = 20, giving W = 30 kg (full water). Then E = 40 - 30 = 10 kg. The empty vessel weighs 10 kg. The other options ignore that the difference of 20 kg corresponds to two-thirds of the water, not the full water.

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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 Ratio & Proportion 60 Clocks & Calendars 56 Sequences & Series 56 Mixtures & Alligation 52 Time & Work 51 Averages 45 Simple & Compound Interest 43 Profit, Loss & Discount 39 Ages 33