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Time and Work — Questions and Answers

Time and Work questions are solved fastest with the unitary method: if A finishes a job in n days, A does 1/n of it per day. Add rates when people work together, subtract when someone works against (a leak, a person undoing work). The LCM method — assume total work equals the LCM of the given days — removes fractions entirely and is the technique most toppers use.

28 solved questionsArithmetic AptitudeFree · no signup

Time and Work— Concepts, Formulas & Shortcuts

  • A finishes in n days ⇒ one day's work = 1/n.
  • Together: 1/A + 1/B = 1/T, so T = AB/(A + B) for two workers.
  • LCM method: let total work = LCM of the days given; each person's daily output becomes a whole number.
  • Efficiency is inversely proportional to time: if A is twice as efficient as B, A takes half the time.
  • M₁D₁H₁/W₁ = M₂D₂H₂/W₂ — the universal men-days-hours-work relation.
  • Work done = rate × time; remaining work = 1 − work already done.

Time and Work Practice Questions with Answers

Attempt each question first, then open the explanation. All 28 questions below are free to read and require no signup.

  1. Q1.A can do a piece of work in 15 days and B in 20 days. Working together they will finish it in:

    Easy
    • A8 4/7 days
    • B9 days
    • C10 days
    • D12 days
    +Show Answer & Explanation

    Answer: A. 8 4/7 days

    Explanation: 1/15 + 1/20 = 4/60 + 3/60 = 7/60 per day → 60/7 = 8 4/7 days.

    Time and Work question 1 of 28

  2. Q2.A and B together complete a work in 8 days. A alone takes 12 days. B alone will take:

    Easy
    • A16 days
    • B20 days
    • C24 days
    • D30 days
    +Show Answer & Explanation

    Answer: C. 24 days

    Explanation: B's rate = 1/8 − 1/12 = 3/24 − 2/24 = 1/24 → 24 days.

    Time and Work question 2 of 28

  3. Q3.10 men complete a work in 12 days. How many days will 15 men take?

    Easy
    • A6 days
    • B8 days
    • C9 days
    • D10 days
    +Show Answer & Explanation

    Answer: B. 8 days

    Explanation: Total = 10 × 12 = 120 man-days. With 15 men: 120/15 = 8 days.

    Time and Work question 3 of 28

  4. Q4.A is twice as good a workman as B and finishes a job 30 days sooner. Working together they finish it in:

    Moderate
    • A15 days
    • B20 days
    • C22 days
    • D25 days
    +Show Answer & Explanation

    Answer: B. 20 days

    Explanation: Let A take x days, then B takes 2x. 2x − x = 30 → x = 30, so A = 30, B = 60. Together: 1/30 + 1/60 = 1/20 → 20 days.

    Time and Work question 4 of 28

  5. Q5.A can do a work in 10 days. He works 4 days and leaves; B finishes the rest in 9 days. B alone would take:

    Moderate
    • A12 days
    • B15 days
    • C18 days
    • D20 days
    +Show Answer & Explanation

    Answer: B. 15 days

    Explanation: A completed 4/10 = 2/5. Remaining 3/5 took B 9 days, so full work takes B 9 × 5/3 = 15 days.

    Time and Work question 5 of 28

  6. Q6.6 men or 8 women can complete a work in 12 days. In how many days will 3 men and 4 women complete it?

    Difficult
    • A10 days
    • B12 days
    • C14 days
    • D15 days
    +Show Answer & Explanation

    Answer: B. 12 days

    Explanation: 6M = 8W ⇒ 1M = 4/3 W. Total work = 8W × 12 = 96 woman-days. 3M + 4W = 4W + 4W = 8W → 96/8 = 12 days.

    Time and Work question 6 of 28

  7. Q7.A, B and C can do a work in 20, 30 and 60 days respectively. Working together they finish it in:

    Easy
    • A9 days
    • B10 days
    • C12 days
    • D15 days
    +Show Answer & Explanation

    Answer: B. 10 days

    Explanation: 1/20 + 1/30 + 1/60 = 3/60 + 2/60 + 1/60 = 6/60 = 1/10 → 10 days.

    Time and Work question 7 of 28

  8. Q8.A does 1/3 of a work in 5 days and B does 2/5 of it in 10 days. Working together they will finish it in:

    Moderate
    • A8 days
    • B9 3/8 days
    • C10 days
    • D11 1/4 days
    +Show Answer & Explanation

    Answer: B. 9 3/8 days

    Explanation: A full work = 15 days, B full work = 25 days. Together: 1/15 + 1/25 = 5/75 + 3/75 = 8/75 → 75/8 = 9 3/8 days.

    Time and Work question 8 of 28

  9. Q9.12 men can complete a work in 8 days. After 6 days, 4 men left. The remaining work was finished in:

    Moderate
    • A2 days
    • B3 days
    • C4 days
    • D5 days
    +Show Answer & Explanation

    Answer: B. 3 days

    Explanation: Total = 96 man-days. In 6 days, 72 done, 24 remain. With 8 men: 24/8 = 3 days.

    Time and Work question 9 of 28

  10. Q10.A can complete a job in 12 days working 8 hours a day, and B in 8 days working 10 hours a day. Working together at 8 hours a day, they finish it in:

    Difficult
    • A4 8/11 days
    • B5 5/11 days
    • C6 days
    • D6 3/11 days
    +Show Answer & Explanation

    Answer: B. 5 5/11 days

    Explanation: A needs 96 hours, B needs 80 hours. Combined hourly rate = 1/96 + 1/80 = 11/480. In an 8-hour day: 88/480 = 11/60 → 60/11 = 5 5/11 days.

    Time and Work question 10 of 28

  11. Q11.A can do a work in 12 days and B in 24 days. Together they finish it in:

    Easy
    • A6 days
    • B8 days
    • C9 days
    • D10 days
    +Show Answer & Explanation

    Answer: B. 8 days

    Explanation: 1/12 + 1/24 = 3/24 = 1/8 → 8 days.

    Time and Work question 11 of 28

  12. Q12.If 20 men can complete a job in 15 days, how many days will 25 men take?

    Easy
    • A10 days
    • B12 days
    • C14 days
    • D18 days
    +Show Answer & Explanation

    Answer: B. 12 days

    Explanation: 20 × 15 = 300 man-days → 300/25 = 12 days.

    Time and Work question 12 of 28

  13. Q13.A is thrice as efficient as B. If together they complete a work in 9 days, A alone will take:

    Moderate
    • A12 days
    • B15 days
    • C18 days
    • D36 days
    +Show Answer & Explanation

    Answer: A. 12 days

    Explanation: Efficiency ratio 3 : 1, so combined 4 parts finish in 9 days → A's 3 parts take 9 × 4/3 = 12 days.

    Time and Work question 13 of 28

  14. Q14.A and B can do a work in 12 days, B and C in 15 days, and A and C in 20 days. All three together will finish it in:

    Difficult
    • A8 days
    • B10 days
    • C12 days
    • D15 days
    +Show Answer & Explanation

    Answer: B. 10 days

    Explanation: Adding all pairs: 2(A+B+C) = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5, so A+B+C = 1/10 → 10 days.

    Time and Work question 14 of 28

  15. Q15.A can do a work in 20 days. He works for 5 days and leaves. B finishes the remaining work in 15 days. B alone would take:

    Moderate
    • A18 days
    • B20 days
    • C24 days
    • D30 days
    +Show Answer & Explanation

    Answer: B. 20 days

    Explanation: A completes 5/20 = 1/4. The remaining 3/4 takes B 15 days, so the full job takes B 15 × 4/3 = 20 days.

    Time and Work question 15 of 28

  16. Q16.15 women can complete a work in 24 days. How many women are needed to finish it in 18 days?

    Moderate
    • A18
    • B20
    • C22
    • D24
    +Show Answer & Explanation

    Answer: B. 20

    Explanation: 15 × 24 = 360 woman-days → 360/18 = 20 women.

    Time and Work question 16 of 28

  17. Q17.A works twice as fast as B. Together they complete a job in 8 days. B alone will take:

    Moderate
    • A12 days
    • B16 days
    • C20 days
    • D24 days
    +Show Answer & Explanation

    Answer: D. 24 days

    Explanation: Efficiency ratio 2 : 1, so 3 parts finish in 8 days → B's 1 part takes 8 × 3 = 24 days.

    Time and Work question 17 of 28

  18. Q18.A and B together can do a work in 10 days. They work together for 4 days, then A leaves and B finishes the rest in 12 days. B alone would take:

    Difficult
    • A16 days
    • B18 days
    • C20 days
    • D24 days
    +Show Answer & Explanation

    Answer: C. 20 days

    Explanation: In 4 days they finish 4/10 = 2/5. B does the remaining 3/5 in 12 days, so B alone needs 12 × 5/3 = 20 days.

    Time and Work question 18 of 28

  19. Q19.If 8 men working 6 hours a day complete a job in 10 days, how many days will 12 men working 8 hours a day take?

    Moderate
    • A4 days
    • B5 days
    • C6 days
    • D8 days
    +Show Answer & Explanation

    Answer: B. 5 days

    Explanation: Total man-hours = 8 × 6 × 10 = 480. With 12 men at 8 h/day: 480/(12 × 8) = 5 days.

    Time and Work question 19 of 28

  20. Q20.A alone can finish a work in 18 days and B in 9 days. B worked for 3 days and left. A alone will finish the remaining work in:

    Moderate
    • A9 days
    • B10 days
    • C12 days
    • D15 days
    +Show Answer & Explanation

    Answer: C. 12 days

    Explanation: B completes 3/9 = 1/3, leaving 2/3. A needs 18 × 2/3 = 12 days.

    Time and Work question 20 of 28

  21. Q21.A can do a work in 6 days and B in 12 days. Together they take:

    Easy
    • A3 days
    • B4 days
    • C5 days
    • D9 days
    +Show Answer & Explanation

    Answer: B. 4 days

    Explanation: 1/6 + 1/12 = 3/12 = 1/4 → 4 days.

    Time and Work question 21 of 28

  22. Q22.If 6 men complete a task in 10 days, 3 men will take:

    Easy
    • A15 days
    • B18 days
    • C20 days
    • D30 days
    +Show Answer & Explanation

    Answer: C. 20 days

    Explanation: 6 × 10 = 60 man-days → 60/3 = 20 days.

    Time and Work question 22 of 28

  23. Q23.A does half a work in 10 days. The full work will take him:

    Easy
    • A15 days
    • B20 days
    • C25 days
    • D30 days
    +Show Answer & Explanation

    Answer: B. 20 days

    Explanation: Half takes 10 days, so the full work takes 20 days.

    Time and Work question 23 of 28

  24. Q24.A and B can complete a work in 6 days. A alone takes 10 days. B alone takes:

    Moderate
    • A12 days
    • B15 days
    • C18 days
    • D20 days
    +Show Answer & Explanation

    Answer: B. 15 days

    Explanation: B's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15 → 15 days.

    Time and Work question 24 of 28

  25. Q25.A can do a work in 30 days and B in 20 days. They work together for 6 days, then A leaves. B finishes the rest in:

    Difficult
    • A8 days
    • B9 days
    • C10 days
    • D12 days
    +Show Answer & Explanation

    Answer: C. 10 days

    Explanation: In 6 days they finish 6(1/30 + 1/20) = 6 × 5/60 = 1/2. B does the remaining 1/2 in 20 × 1/2 = 10 days.

    Time and Work question 25 of 28

  26. Q26.If 4 taps fill a tank in 10 hours, 5 taps will fill it in:

    Easy
    • A6 hours
    • B7 hours
    • C8 hours
    • D9 hours
    +Show Answer & Explanation

    Answer: C. 8 hours

    Explanation: 4 × 10 = 40 tap-hours → 40/5 = 8 hours.

    Time and Work question 26 of 28

  27. Q27.A is 50% more efficient than B. If B takes 30 days, A takes:

    Moderate
    • A15 days
    • B18 days
    • C20 days
    • D25 days
    +Show Answer & Explanation

    Answer: C. 20 days

    Explanation: Efficiency ratio A : B = 3 : 2, so time ratio is 2 : 3 → A takes 30 × 2/3 = 20 days.

    Time and Work question 27 of 28

  28. Q28.Three workers can finish a job in 12, 18 and 36 days. Working together they take:

    Moderate
    • A5 days
    • B6 days
    • C8 days
    • D9 days
    +Show Answer & Explanation

    Answer: B. 6 days

    Explanation: 1/12 + 1/18 + 1/36 = 3/36 + 2/36 + 1/36 = 6/36 = 1/6 → 6 days.

    Time and Work question 28 of 28

Time and Work — Frequently Asked Questions

What is the LCM method in time and work?+

Instead of fractions, set the total work equal to the LCM of all the given times. If A takes 15 days and B takes 20, total work = 60 units; A does 4 units/day and B does 3, so together they do 7 units/day and finish in 60/7 days.

How do negative (leak) rates work?+

A leak or an outlet pipe subtracts from the combined rate. If filling rate is 1/8 and the leak empties at 1/40, the net rate is 1/8 − 1/40 = 1/10.

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