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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 for 10 days when B and C leave.
How many days more will A take to complete the work?
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- 16 days
- 15 days
- 18 days
- 20 days
Correct Option: C
Using Rule 3,
| (A + B)’s 1 day’s work = | 30 |
| (B + C)’s 1 day’s work = | 24 |
| (C + A)’s 1 day’s work = | 20 |
Adding all the above, we have
2 ( A + B + C)’s 1 day’s work
| = | + | + | ||||
| 30 | 24 | 20 |
| = | = | = | ||||
| 120 | 120 | 8 |
∴ (A + B + C)’s 1 day’s work
| = | = | |||
| 8 × 2 | 16 |
Now, all three worked together for 10 days.
∴ (A + B + C)’s 10 days’ work
| = | × 10 = | |||
| 16 | 8 |
∴ Remaining part of work
| = 1 - | = | = | ||||
| 8 | 8 | 8 |
Now, A’s 1 day’s work
| = | - | = | = | |||||
| 16 | 24 | 48 | 48 |
Since, A finishes 1/48 part of work in 1 day
∴ A will finish 3/8 part of work in
| 1 × 48 × | = 18 days. | 8 |
