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A and B can do a piece of work in 30 days while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work ?
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- 18 days
- 24 days
- 30 days
- 36 days
Correct Option: A
| (A + B)’s day’s work = | 30 |
| (B + C)’s 1 day’s work = | 24 |
| (C + A)’s 1 day’s work = | 20 |
∴ 2 (A + B + C)’s 1 day’s work
| = | + | + | ||||
| 30 | 24 | 20 |
| = | = | = | ||||
| 120 | 120 | 8 |
∴ (A + B + C)’s 1 day’s work
| = | 16 |
∴ (A + B + C)’s 10 days’ work
| = | = | |||
| 16 | 8 |
| ∴ Remaining work = 1 - | = | |||
| 8 | 8 |
This part of work is done by A alone.
| Now A’s 1 day’s work = | - | |||
| 16 | 24 |
| = | = | |||
| 48 | 48 |
∴ The required no. of days
| = | × 48 = 18 days | 8 |
