Pariksha SaathiQuantitative Aptitude
Time and Work: Practice Questions with Answers
14 practice questions on Time and Work, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.1
A can complete a work in 10 days and B can complete the same work in 15 days. If they work together, in how many days will they finish it?
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Answer: 6 days
Solution:
- A’s rate = 1/10, B’s rate = 1/15 per day.
- Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 of the work per day.
- Time to finish together = 1 ÷ (1/6) = 6 days.
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Q.2
12 men can build a wall in 15 days. How many men, working at the same rate, are needed to build it in 10 days?
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Answer: 18 men
Solution:
- For the same total work, Men × Days stays constant: 12 × 15 = 180.
- For 10 days: Men = 180 / 10
- = 18 men
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Q.3
A and B together can complete a work in 12 days. A alone can complete it in 20 days. In how many days can B alone complete the work?
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Answer: 30 days
Solution:
- Combined rate (A + B) = 1/12. A’s rate = 1/20.
- B’s rate = 1/12 − 1/20 = 5/60 − 3/60 = 2/60 = 1/30 of the work per day.
- B’s time alone = 1 ÷ (1/30) = 30 days.
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Q.4
A can finish a work in 10 days and B in 15 days. They work on alternate days, starting with A. In how many days will the work finish?
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Answer: 12 days
Solution:
- A's rate = 1/10, B's rate = 1/15. In each 2-day cycle (one day A, one day B), work done = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6.
- After 6 cycles (12 days), work done = 6 × 1/6 = 1 — exactly the whole job, with no leftover day to analyse.
- So the work finishes in exactly 12 days.
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Q.5
A can complete a piece of work in 12 days. What fraction of the work does he complete in 4 days?
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Answer: 1/3 of the work
Solution:
- A’s rate = 1/12 of the work per day.
- Work done in 4 days = 4 × (1/12) = 4/12
- = 1/3
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Q.6
A can do a piece of work in 20 days. B is 25% more efficient than A. Find the number of days B alone takes to complete the same work.
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Answer: 16 days
Solution:
- "25% more efficient" means B’s work rate is 1.25 times A’s rate.
- Since time is inversely proportional to rate, B’s time = A’s time ÷ 1.25 = 20 ÷ 1.25
- = 16 days
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Q.7
A and B together can complete a work in 12 days. They work together for 4 days, after which A leaves, and B alone completes the remaining work in 16 more days. In how many days could B alone have completed the entire work?
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Answer: 24 days
Solution:
- Combined rate = 1/12. Work done in the first 4 days = 4 × 1/12 = 1/3.
- Remaining work = 1 − 1/3 = 2/3, and B alone finishes this in 16 days, so B's rate = (2/3) / 16 = 1/24.
- B alone would take 1 ÷ (1/24) = 24 days for the entire work.
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Q.8
A can finish a work in 8 days and B in 12 days. They work on alternate days, starting with A. In how many days will the work be completed?
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Answer: 9.5 days. 4 full cycles (8 days) complete 5/6 of the work; day 9 (A) adds 1/8, leaving 1/24; B finishes that 1/24 in half a day at B's rate of 1/12 per day.
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Q.9
A can complete a work in 6 days and B can complete the same work in 12 days. Working together, how many days will they take?
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Q.10
A and B can together finish a work in 15 days. They work together for 5 days, then A leaves and B alone finishes the remaining work in 20 more days. Find how long B alone would take for the entire work.
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Answer: 30 days. Work done together in 5 days = 1/3; remaining 2/3 takes B 20 days, so B's rate = 1/30.
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Q.11
A and B together can complete a work in 15 days. B alone can complete it in 25 days. In how many days can A alone complete the work?
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Q.12
15 men can complete a job in 8 days. How many men, at the same rate, are needed to complete it in 6 days?
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Q.13
A can complete a work in 8 days. What fraction of the work does he complete in 3 days?
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Q.14
A can do a work in 18 days and B in 24 days. They work together for 8 days. What fraction of the work remains?
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Answer: 2/9. Combined rate = 1/18 + 1/24 = 7/72; work done in 8 days = 56/72 = 7/9; remaining = 2/9.
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-01.