1. Basic idea
If A finishes work in a days, A's 1-day work = 1/a. Together A and B: 1/a + 1/b → time = ab/(a + b).
2. LCM (efficiency) method — fastest
Take total work = LCM of the days. Efficiency = work/days.
A 12 days, B 18 days → work = 36 units; A = 3/day, B = 2/day; together 5/day → 7.2 days.
3. Formulas
| Case | Result |
|---|---|
| A and B together in T, A alone in a | B = aT/(a − T) |
| A, B, C together | 1/(1/a + 1/b + 1/c) |
| A + B in x, B + C in y, C + A in z | All three = 2xyz/(xy + yz + zx) |
| A is k times as efficient as B | A takes 1/k of B's time |
| Chain rule | M₁D₁H₁/W₁ = M₂D₂H₂/W₂ |
4. Solved examples
(ASO 2015) A and B in 12 days, B alone 30 → A = 1/12 − 1/30 = 1/20 → 20 days.
(ASO 2021) A in 18, B in 15; B works 10 days → 2/3 done; A finishes 1/3 in 6 days.
A is twice as fast as B; together 12 days → B alone 36 days, A alone 18 days.
12 men or 18 women do a job in 14 days → 8 men + 16 women: 1 man = 1.5 women → 28 women-units vs 18 × 14 = 252 → 9 days.
A works alternate days with B (A starts), A 6 days, B 12 days → 2-day cycle does 1/4 → 4 cycles = 8 days.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. A can do a piece of work in 12 days and B in 24 days. In how many days can they finish it working together?
(a) 12 days (b) 8 days (c) 10 days (d) 18 days
Answer: (b) 8 days
Solution: Work = LCM(12, 24) = 24 units. A = 2/day, B = 1/day. Together = 24/3 = 8 days.
Example 2. A can finish a job in 12 days and B in 20 days. What part of the job do they finish together in one day?
(a) 1/32 (b) 1/240 (c) 4/15 (d) 2/15
Answer: (d) 2/15
Solution: 1/12 + 1/20 = 2/15.
Example 3. A can finish a job in 8 days and B in 24 days. What part of the job do they finish together in one day?
(a) 1/6 (b) 1/192 (c) 1/32 (d) 1/3
Answer: (a) 1/6
Solution: 1/8 + 1/24 = 1/6.
Example 4. 15 men can build a wall in 20 days. How many days will 10 men take to build the same wall?
(a) 15 1/3 days (b) 34 days (c) 13 1/3 days (d) 30 days
Answer: (d) 30 days
Solution: Men × days is constant: 15 × 20 = 300 man-days. 300/10 = 30 days.
Example 5. 24 men can build a wall in 10 days. How many days will 30 men take to build the same wall?
(a) 14 1/2 days (b) 8 days (c) 12 days (d) 12 1/2 days
Answer: (b) 8 days
Solution: Men × days is constant: 24 × 10 = 240 man-days. 240/30 = 8 days.
Example 6. A and B together can finish a work in 10 days. B alone can do it in 30 days. A alone can do it in:
(a) 23 days (b) 17 days (c) 15 days (d) 20 days
Answer: (c) 15 days
Solution: A's rate = 1/10 − 1/30 = 1/15. So A alone takes 15 days. (Type asked in OPSC ASO 2015.)
Example 7. A is 2 times as efficient as B. B alone can finish a work in 24 days. In how many days can A and B together finish it?
(a) 11 days (b) 8 days (c) 12 days (d) 6 days
Answer: (b) 8 days
Solution: A takes 24/2 = 12 days. Together = 24×12/(24+12) = 8 days.
ASO exam level
Example 8. A, B and C can do a work in 6, 8 and 12 days respectively. Working together, they will finish it in:
(a) 2 2/3 days (b) 3 2/3 days (c) 8 2/3 days (d) 5 1/3 days
Answer: (a) 2 2/3 days
Solution: Work = 24 units. Rates 4 + 3 + 2 = 9/day. Time = 24/9 = 2.67 days.
Example 9. A, B and C can do a work in 20, 30 and 60 days respectively. Working together, they will finish it in:
(a) 36 2/3 days (b) 20 days (c) 11 days (d) 10 days
Answer: (d) 10 days
Solution: Work = 60 units. Rates 3 + 2 + 1 = 6/day. Time = 60/6 = 10 days.
Example 10. A and B can do a work in 10 and 15 days. They work together for 4 days, then A leaves. In how many more days will B finish the rest?
(a) 7 days (b) 3 1/3 days (c) 5 days (d) 11 days
Answer: (c) 5 days
Solution: Work = 30 units; A = 3/day, B = 2/day. In 4 days: 20 units. Left 10 → B takes 10/2 = 5 days.
Example 11. A and B can do a work in 10 and 15 days. They work together for 2 days, then A leaves. In how many more days will B finish the rest?
(a) 12 days (b) 10 days (c) 13 days (d) 6 2/3 days
Answer: (b) 10 days
Solution: Work = 30 units; A = 3/day, B = 2/day. In 2 days: 10 units. Left 20 → B takes 20/2 = 10 days.
Example 12. One man does as much work as 2 women. 3 men can finish a job in 20 days. In how many days will 3 men and 4 women finish it?
(a) 14 days (b) 8 4/7 days (c) 12 days (d) 10 days
Answer: (c) 12 days
Solution: 4 women = 2 men. Total = 5 men. Days = 3×20/5 = 12.
Example 13. One man does as much work as 2 women. 3 men can finish a job in 24 days. In how many days will 3 men and 4 women finish it?
(a) 16 2/5 days (b) 14 2/5 days (c) 10 2/7 days (d) 12 days
Answer: (b) 14 2/5 days
Solution: 4 women = 2 men. Total = 5 men. Days = 3×24/5 = 14.4.
Example 14. A can do a work in 8 days and B in 12 days. They work on alternate days, A starting first. In how many days will the work be finished?
(a) 10 1/2 days (b) 4 4/5 days (c) 9 days (d) 9 1/2 days
Answer: (d) 9 1/2 days
Solution: Work = 24 units; A = 3, B = 2 per day. Every 2 days: 5 units. 4 pairs = 20 units in 8 days; the rest (4) takes 1.5 more day(s). Total 9.5 days.
Example 15. A can do a work in 10 days and B in 15 days. They work on alternate days, A starting first. In how many days will the work be finished?
(a) 13 days (b) 11 1/2 days (c) 6 days (d) 12 days
Answer: (d) 12 days
Solution: Work = 30 units; A = 3, B = 2 per day. Every 2 days: 5 units. 6 pairs = 30 units in 12 days; the rest (0) takes 0 more day(s). Total 12 days.
Advanced level
Example 16. A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days. C alone can do it in:
(a) 10 days (b) 15 2/3 days (c) 70 days (d) 60 days
Answer: (d) 60 days
Solution: 2(A + B + C) = 1/12 + 1/15 + 1/20 → A + B + C = 1/10. C = 1/10 − 1/12 = 1/60. C alone: 60 days.
Example 17. A can finish a work in 15 days and B in 25 days. A starts alone and B joins him after 4 days. In how many days in total is the work finished?
(a) 12 7/8 days (b) 6 7/8 days (c) 9 3/8 days (d) 10 7/8 days
Answer: (d) 10 7/8 days
Solution: Work = 75. A does 20 units in 4 days. Left 55 at 8/day → 6.88 days. Total = 10.88 days.
Topic-wise practice for Time and work (Quant): Efficiency, M1D1 = M2D2, worker leaves or joins, men-women-boys. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- Work per day (A alone, B alone, together)
- A + B, B + C, C + A type
- Efficiency ratio
- M1D1H1 = M2D2H2
- Worker leaves or joins midway
- Men, women and boys
- Alternate days working
- Work and wages shared by work done