Time and Work: 20 Practice Questions with Solutions – each with step-by-step solutions

Time and Work : 20 Practice Questions with Solutions – each with step-by-step solutions

Time and Work

Here are a few questions on Time and Work from Basic to hard. Practice many such questions on a daily basis.

🔹 Basic Level

1. A can do a piece of work in 10 days. How much work does A do in one day?
Solution:
Work per day = 1/10

2. B can do a job in 5 days. What is B’s efficiency?
Solution:
Efficiency = 1/5

3. A can do a job in 10 days, B in 20 days. How long will they take together?
Solution:
A’s rate = 1/10, B’s rate = 1/20
Combined rate = 3/20
Time = 1 ÷ (3/20) = 6.67 days

4. A can do a work in 12 days. B can do the same in 18 days. How long together?
Solution:
A = 1/12, B = 1/18
LCM = 36 → A = 3 units/day, B = 2 units/day
Total = 5 units/day → Time = 36/5 = 7.2 days

5. A and B together can do a job in 8 days. A alone can do it in 12 days. How long will B take alone?
Solution:
A = 1/12, A+B = 1/8
B = 1/8 – 1/12 = (3 – 2)/24 = 1/24
Time = 24 days

🔹 Intermediate Level

6. A can do a job in 15 days. B is twice as efficient. How long will B take?
Solution:
B’s efficiency = 2 × A = 2/15
Time = 1 ÷ (2/15) = 7.5 days

7. A and B can do a job in 10 days. B and C in 12 days. A and C in 15 days. How long will A, B, and C take together?
Solution:
Add all: (A+B) + (B+C) + (A+C) = 1/10 + 1/12 + 1/15 = 47/60
2(A+B+C) = 47/60 → A+B+C = 47/120
Time = 1 ÷ (47/120) = 120/47 ≈ 2.55 days

8. A can do a job in 10 days. B joins after 2 days. Together they finish in 6 days. How long will B take alone?
Solution:
A’s 2-day work = 2/10 = 1/5
Remaining = 4/5
A+B = 4/5 in 4 days → rate = 1/5
A = 1/10 → B = 1/5 – 1/10 = 1/10
Time = 10 days

9. A can do a job in 6 days. B in 12 days. C in 18 days. How long will they take together?
Solution:
A = 1/6, B = 1/12, C = 1/18
Total = (6 + 3 + 2)/36 = 11/36
Time = 1 ÷ (11/36) = 3.27 days

10. A does 1/3 of a job in 5 days. How long to complete full job?
Solution:
Time = 5 × 3 = 15 days

🔹 Advanced Level

11. A and B can do a job in 10 days. B and C in 15 days. C and A in 20 days. Find time for A, B, and C together.
Solution:
Add all: (A+B) + (B+C) + (C+A) = 1/10 + 1/15 + 1/20 = 17/60
2(A+B+C) = 17/60 → A+B+C = 17/120
Time = 1 ÷ (17/120) = 120/17 ≈ 7.06 days

12. A can do a job in 10 days. B in 15 days. C in 30 days. They work together for 2 days. How much work is left?
Solution:
Total rate = 1/10 + 1/15 + 1/30 = 1/4
Work in 2 days = 2 × 1/4 = 1/2
Remaining = 1/2

13. A and B can do a job in 12 days. B and C in 15 days. A and C in 20 days. Find B’s time alone.
Solution:
Use equations or substitution method.
Let A+B = 1/12, B+C = 1/15, A+C = 1/20
Add all: 2(A+B+C) = 1/12 + 1/15 + 1/20 = 37/60
A+B+C = 37/120
Now B = A+B+C – A – C = 37/120 – (1/20 + 1/20) = 37/120 – 1/10 = 25/120 = 5/24
Time = 1 ÷ (5/24) = 4.8 days

14. A can do a job in 8 days. B in 12 days. C in 16 days. They work together. How long to finish?
Solution:
Rate = 1/8 + 1/12 + 1/16 = LCM = 48
→ (6 + 4 + 3)/48 = 13/48
Time = 48/13 = 3.69 days

15. A and B can do a job in 10 days. A alone in 15 days. B alone in?
Solution:
A = 1/15, A+B = 1/10
B = 1/10 – 1/15 = 1/30
Time = 30 days

16. A can do a job in 20 days. B in 30 days. C in 60 days. How long together?
Solution:
Rate = 1/20 + 1/30 + 1/60 = (3 + 2 + 1)/60 = 6/60 = 1/10
Time = 10 days

17. A and B together can do a job in 6 days. B and C in 8 days. A and C in 12 days. Find time for A, B, C together.
Solution:
Add all: (A+B) + (B+C) + (A+C) = 1/6 + 1/8 + 1/12 = 13/24
2(A+B+C) = 13/24 → A+B+C = 13/48
Time = 1 ÷ (13/48) = 3.69 days

18. A can do a job in 10 days. B in 15 days. They work together for 3 days. How much work is done?
Solution:
Rate = 1/10 + 1/15 = 1/6
Work = 3 × 1/6 = 1/2

19. A can do a job in 10 days. B in 20 days. C in 40 days. How long together?
Solution:
Rate = 1/10 + 1/20 + 1/40 = (4 + 2 + 1)/40 = 7/40
Time = 40/7 = 5.71 days

20. A can do a job in 5 days. B in 10 days. C in 20 days. They work together for 2 days. How much work is left?
Solution:
Rate = 1/5 + 1/10 + 1/20 = (4 + 2 + 1)/20 = 7/20
Work in 2 days = 2 × 7/20 = 14/20 = 0.7
Remaining = 1 – 0.7 = 0.3 or 3/10

Tricks for Time and Work will be posted in the next lesson.