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Time and Work, Pipes and Cisterns MCQs

Solved mathematics MCQs on time and work, efficiency, man-days, wages, alternate-day work, pipes, outlets and leaks, with the LCM shortcut, for PPSC, FPSC and NTS tests.

20 MCQsUpdated 30 October 2026

These MCQs cover work done by two or more people, efficiency, man-days, sharing wages, working on alternate days, and pipes and cisterns with inlets, outlets and leaks.

The easiest method is to take the total work as the LCM of the given days and work in whole units per day, which the explanations show step by step. Every answer was calculated and checked by script.

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  1. 1

    Ali can finish a piece of work in 12 days and Bilal in 18 days. In how many days can they finish it together?

    Correct answer: B. 7.2 days

    Take the work as 36 units (LCM of 12 and 18): Ali does 3 units a day and Bilal 2, so together 5 a day; 36 ÷ 5 = 7.2 days.

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    medium
  2. 2

    A, B and C can do a job alone in 10, 15 and 30 days. How long will they take working together?

    Correct answer: A. 5 days

    Take 30 units: A does 3, B 2 and C 1 unit a day, 6 together; 30 ÷ 6 = 5 days.

    easy
  3. 3

    A and B together finish a task in 6 days; A alone needs 10 days. How long does B alone need?

    Correct answer: B. 15 days

    Take 30 units: together they do 5 a day and A does 3, so B does 2 a day; 30 ÷ 2 = 15 days.

    medium
  4. 4

    Sana is three times as efficient as Hira. Together they complete a project in 12 days. How long would Hira take alone?

    Correct answer: C. 48 days

    If Hira does 1 unit a day, Sana does 3: together 4 a day, so the work is 4 × 12 = 48 units. Hira alone needs 48 ÷ 1 = 48 days.

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    hard
  5. 5

    18 labourers can build a wall in 20 days. How many days will 24 labourers take?

    Correct answer: C. 15 days

    Work = 18 × 20 = 360 labourer-days; 360 ÷ 24 = 15 days.

    easy
  6. 6

    16 men can dig a canal in 15 days. How many men are needed to dig it in 10 days?

    Correct answer: D. 24

    Work = 16 × 15 = 240 man-days; 240 ÷ 10 = 24 men.

    easy
  7. 7

    A can do a work in 20 days and B in 30 days. They work together for 5 days, then A leaves. How many more days does B need to finish it?

    Correct answer: A. 17.5 days

    Take 60 units: A does 3 and B 2 a day. In 5 days they do 25 units, leaving 35; B needs 35 ÷ 2 = 17.5 days.

    hard
  8. 8

    A can do a job in 8 days and B in 24 days. They do it together and receive Rs. 9,000. What is A's share?

    Correct answer: C. Rs. 6,750

    Wages follow work done. Of 24 units, A does 3 a day and B 1, a 3 : 1 ratio, so A gets 3/4 × 9,000 = Rs. 6,750.

    medium
  9. 9

    Pipe A can fill a tank in 20 minutes and pipe B in 30 minutes. How long will both together take to fill it?

    Correct answer: B. 12 minutes

    Take 60 units: A fills 3 and B 2 units a minute, 5 together; 60 ÷ 5 = 12 minutes.

    easy
  10. 10

    A pipe fills a tank in 6 hours, while an outlet empties the full tank in 9 hours. If both are open, how long will the tank take to fill?

    Correct answer: C. 18 hours

    Take 18 units: the inlet adds 3 and the outlet removes 2 units an hour, a net gain of 1; 18 ÷ 1 = 18 hours.

    medium
  12. 11

    Two pipes fill a tank in 10 and 15 hours, and a third pipe empties it in 30 hours. If all three are opened together, how long will the tank take to fill?

    Correct answer: B. 7.5 hours

    Take 30 units: the two pipes add 3 + 2 and the third removes 1, a net 4 units an hour; 30 ÷ 4 = 7.5 hours.

    hard
  13. 12

    A tap fills a tank in 6 hours, but because of a leak it takes 8 hours. How long would the leak take to empty the full tank?

    Correct answer: D. 24 hours

    Take 24 units: the tap fills 4 an hour, but only 3 are gained, so the leak removes 1 unit an hour and empties the tank in 24 hours.

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    hard
  14. 13

    A tap fills an empty tank in 40 minutes. How long will it take to fill the tank when it is already half full?

    Correct answer: A. 20 minutes

    Half the tank remains, so it needs half of 40 minutes: 20 minutes.

    easy
  15. 14

    A can do a work in 9 days and B in 18 days. If they work on alternate days, starting with A, in how many days will the work be finished?

    Correct answer: B. 12 days

    Take 18 units: A does 2 and B 1, so each pair of days gives 3 units. Six pairs (12 days) finish exactly 18 units.

    hard
  16. 15

    4 men or 6 women can finish a job in 20 days. How long will 2 men and 3 women take to finish it?

    Correct answer: C. 20 days

    4 men = 6 women, so 1 man = 1.5 women and 2 men + 3 women = 6 women, who take 20 days.

    medium
  17. 16

    10 men working 6 hours a day finish a job in 12 days. How many days will 8 men take working 9 hours a day?

    Correct answer: C. 10 days

    Work = 10 × 6 × 12 = 720 man-hours; 8 men × 9 hours = 72 man-hours a day, so 720 ÷ 72 = 10 days.

    medium
  18. 17

    A finishes one-third of a job in 5 days. How many days will A take to finish the whole job?

    Correct answer: D. 15 days

    One-third takes 5 days, so the whole job takes 3 × 5 = 15 days.

    easy
  19. 18

    A takes 15 days to finish a job. B is 50% more efficient than A. How many days will B take?

    Correct answer: A. 10 days

    B does 1.5 times as much work a day, so B needs 15 ÷ 1.5 = 10 days.

    medium
  20. 19

    A and B can do a job in 8 days, B and C in 12 days, and A and C in 24 days. How long will A, B and C take together?

    Correct answer: B. 8 days

    Take 24 units: the pairs do 3, 2 and 1 units a day, so 2(A + B + C) = 6 and A + B + C = 3 units a day; 24 ÷ 3 = 8 days.

    hard
  21. 20

    Two outlet pipes can empty a full tank in 12 and 24 minutes. How long will they take to empty it together?

    Correct answer: C. 8 minutes

    Take 24 units: they remove 2 and 1 units a minute, 3 together; 24 ÷ 3 = 8 minutes.

    easy