Question: 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?
[A].18 days
24 days
30 days
36 days
[A].
[B].
[C].
[D].
Answer: Option A
Explanation:
| 2(A + B + C)’s 1 day’s work = | 1 | + | 1 | + | 1 | = | 15 | = | 1 | . | ||
| 30 | 24 | 20 | 120 | 8 |
| Therefore, (A + B + C)’s 1 day’s work = | 1 | = | 1 | . |
| 2 x 8 | 16 |
| Work done by A, B, C in 10 days = | 10 | = | 5 | . |
| 16 | 8 |
| Remaining work = | 1 – | 5 | = | 3 | . | ||
| 8 | 8 |
| A’s 1 day’s work = | 1 | – | 1 | = | 1 | . | ||
| 16 | 24 | 48 |
| Now, | 1 | work is done by A in 1 day. |
| 48 |
| So, | 3 | work will be done by A in | 48 x | 3 | = 18 days. | ||
| 8 | 8 |