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A can do a piece of work in 120 days and B can do it in 150 days. They work together for 20 days. Then B leaves and A alone continues the work. 12 days after that C joins A and the work is completed in 48 days more. In how many days can C do it if he works alone?
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- 230 days
- 225 days
- 240 days
- 220 days
Correct Option: C
A’s 1 day’s work
| = | 120 |
| B’s 1 day’s work = | 150 |
(A + B)’s 1 day’s work
| = | + | = | = | |||||
| 120 | 150 | 600 | 200 |
(A + B) work together for 20 days
Hence, (A + B)’s 20 days’ work
| = 20 × | = | |||
| 200 | 10 |
After 20 days B leaves, and A alone works for 12 days
∴ A’s 12 days’ work
| = | × 12= | |||
| 120 | 10 |
Now, after 12 days, C joins A and the work is finished in 48 days. It means A works for 48 days more.
∴ A’s 48 days’ work
| = | × 48 = | |||
| 120 | 5 |
∴ Total work done by A and B together
| = | + | + | ||||
| 10 | 10 | 5 |
| = | = | |||
| 10 | 5 |
∴ Remaining work
| = 1 - | = | |||
| 5 | 5 |
This part of work, i.e., 1/5 is done by C in 48 days
| ∴ C’s 48 days’ work = | 5 |
∴ C’s 1 day’s work
| = | = | |||
| 5 × 48 | 240 |
Hence, C alone can finish the work in 240 days.
