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A can complete a work in 10 days, B can complete the same work in 20 days and C in 40 days. A starts working on the first day, B works for second day and C works for third day. Again A works for fourth day and B for fifth day and so on. If they continued working in the same way, in how many days will the work be completed?
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- 15 days
- 16.5 days
- 15.5 days
- 17 days
Correct Option: B
A’s work for the first day
| = | 10 |
B’s work for the second day
| = | 20 |
C’s work for the third day
| = | 40 |
Work done in 3 days by them together
| = | + | + | ||||
| 10 | 20 | 40 |
| = | = | |||
| 40 | 40 |
Hence, 7/40 part of work will be completed in 3 days.
| = | i.e | |||
| 40 | 40 |
part of work will be completed in 3 × 5 or 15 days.
Remaining work
| = 1 - | = | = | ||||
| 40 | 40 | 8 |
Now, A will work on 16th day.
The remaining work after 16 days
| = | - | = | = | |||||
| 8 | 10 | 40 | 40 |
Again, B will work on 17th day.
∵ B completes the work in 20 days.
∴ B will complete 1/40 part of work in
| = 20 × | = | day | ||
| 40 | 2 |
Hence, Total time taken in completion of work
| = 15 + 1 + | = 16 | day | ||
| 2 | 2 |
