Time & Work / Pipes & Cisterns

LSSSSB Non-Technical · Mathematics · 53 practice questions with answers and explanations: 14 Easy, 38 Medium, 1 Hard.

Sample questions

Sample Easy question 1

A and B can do a work together in 15 days. A alone can do it in 25 days. Find B's time alone.

  1. 36
  2. 40
  3. 35
  4. 37.5
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Answer: D. B's rate = 1/15 - 1/25 = 2/75, so B alone takes 37.5 days.

Sample Easy question 2

If 8 men can build a wall in 15 days, how many days will 12 men take?

  1. 8
  2. 11
  3. 10
  4. 9
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Answer: C. Total work = 8×15 = 120 man-days; 12 men take 120/12 = 10 days.

Sample Easy question 3

A can do a piece of work in 4 days and B in 12 days. In how many days can they finish it together?

  1. 4 days
  2. 5 days
  3. 3 days
  4. 2 days
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Answer: C. Combined rate = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3, so together they take 3 days.

Sample Medium question 4

A and B together can finish a job in 6 days. If A alone can finish it in 10 days, in how many days can B alone finish it?

  1. 18 days
  2. 20 days
  3. 15 days
  4. 12 days
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Answer: C. B's rate = 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15, so B alone takes 15 days.

Sample Medium question 5

A works on a task for 4 days and then leaves. B finishes the remaining work in 6 days. If A alone could do the whole task in 12 days, how many days would B alone take?

  1. 12 days
  2. 9 days
  3. 10 days
  4. 8 days
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Answer: B. A's work in 4 days = 4/12 = 1/3. Remaining 2/3 is done by B in 6 days, so B's rate = (2/3)/6 = 1/9, meaning B alone takes 9 days.

Sample Medium question 6

A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both are opened together, how long will it take to fill the tank?

  1. 22 hours
  2. 20 hours
  3. 24 hours
  4. 26 hours
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Answer: C. Net rate = 1/6 - 1/8 = 4/24 - 3/24 = 1/24, so the tank fills in 24 hours.

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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