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Ladakh Police Sub-Inspector · Mathematics · 53 practice questions with answers and explanations: 14 Easy, 38 Medium, 1 Hard.

Sample questions

Sample Easy question 1

6 men can complete a work in 12 days. How many days will 8 men take?

  1. 10
  2. 11
  3. 8
  4. 9
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Answer: D. Total work = 6 × 12 = 72 man-days. For 8 men: 72/8 = 9 days.

Sample Easy question 2

A can finish a job in 8 days. After working for 4 days, what fraction of the job is done?

  1. 1/2
  2. 1/4
  3. 2/3
  4. 1/3
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Answer: A. In 4 days, A does 4/8 = 1/2 of the work.

Sample Easy question 3

If 5 workers can complete a task in 12 days, how many days will 10 workers take?

  1. 5
  2. 4
  3. 7
  4. 6
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Answer: D. Doubling the workers halves the time: 12/2 = 6 days.

Sample Medium question 4

A, B and C can complete a piece of work in 15, 24 and 60 days respectively. They start together. After 1 day A leaves, and after 3 more days C also leaves. In how many more days will B finish the remaining work?

  1. 17 4/5 days
  2. 15 4/5 days
  3. 16 4/5 days
  4. 18 4/5 days
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Answer: C. Work done in the first 1 day(s) = 1 × 1/8; work done in the next 3 day(s) by B and C = 3 × 7/120. Remaining work = 7/10, which B alone does in 16 4/5 days.

Sample Medium question 5

A, B and C can complete a piece of work in 20, 24 and 60 days respectively. They start together. After 2 days A leaves, and after 1 more day C also leaves. In how many more days will B finish the remaining work?

  1. 18 2/5 days
  2. 17 2/5 days
  3. 16 2/5 days
  4. 19 2/5 days
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Answer: B. Work done in the first 2 day(s) = 2 × 13/120; work done in the next 1 day(s) by B and C = 1 × 7/120. Remaining work = 29/40, which B alone does in 17 2/5 days.

Sample Medium question 6

A, B and C can complete a piece of work in 30, 20 and 15 days respectively. They start together. After 1 day A leaves, and after 1 more day C also leaves. In how many more days will B finish the remaining work?

  1. 16 2/3 days
  2. 14 2/3 days
  3. 13 2/3 days
  4. 15 2/3 days
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Answer: B. Work done in the first 1 day(s) = 1 × 3/20; work done in the next 1 day(s) by B and C = 1 × 7/60. Remaining work = 11/15, which B alone does in 14 2/3 days.

Sample Hard question 7

Together, A and B take 18 days to finish a job; A does half as much work as B in three-fourths of B's time. Find B's time alone.

  1. 25
  2. 30
  3. 28
  4. 32
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Answer: B. Working through the ratio gives A's rate as 2/(3x) where x is B's time; solving the combined rate equation gives x = 30 days.

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