-
A can complete a work in 24 days, B in 32 days and C in 64 days. They start together. A works for 6 days and leaves and B leaves 6 days before the work is finished. In how many days was the work finished?
-
- 20 days
- 21 days
- 22 days
- 25 days
Correct Option: A
Let the work was completed in x days. Hence, A worked for 6 days, B worked for (x – 6) days and C worked for x days.
| Now, A’s 1 day’s work = | 24 |
∴ A’s 6 days’ work
| = | × 6 = | |||
| 24 | 4 |
| B’s 1 day’s work = | 32 |
∴ B’s (x – 6) days’ work
| = | × (x - 6) = | |||
| 32 | 32 |
| C’s 1 day’s work = | 64 |
∴ C’s x days’ work
| = | × x = | |||
| 64 | 64 |
| ∴ | + | + | = 1 | |||
| 4 | 32 | 64 |
| ⇒ | + | |||
| 32 | 64 |
| = 1 - | = | |||
| 4 | 4 |
⇒ 3x – 12 = 48
⇒ 3x = 48 + 12 = 60
| ⇒ x = | = 20 | 3 |
Hence, the work was completed in 20 days
