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A, B and C can complete a work separately in 24, 36 and 48 days respectively. They started together but C left after 4 days of start and A left 3 days before the completion of work. In how many days will the work be completed?
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- 20 days
- 18 days
- 16 days
- 15 days
Correct Option: D
Let the work be completed in x days. Therefore, A worked for x – 3 days, B for x days and C for 4 days.
| A’s 1 day’s work = | 24 |
| B’s 1 day’s work = | 36 |
| and, C’s 1 day’s work = | 48 |
| ∴ (x - 3) × | + x × | + 4 × | = 1 | |||
| 24 | 36 | 48 |
| ⇒ | + | + | = 1 | |||
| 24 | 36 | 12 |
| ⇒ | = 1 | 72 |
⇒ 5x – 3 = 72
⇒ 5x = 75
| ⇒ x = | = 15 | 5 |
Hence, the work was completed in 15 days.
