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A and B can do a piece of work in 12 days, B and C in 15 days; C and A in 20 days. In how many days will they finish it working together? In what time can A do it separately?
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- 45 days
- 20 days
- 60 days
- 30 days
Correct Option: D
(A + B)’s 1 day’s work
| = | 12 |
(B + C)’s 1 day’s work
| = | 15 |
(C + A)’s 1 day’s work
| = | 20 |
Adding all,
2 (A + B + C)’s 1 day’s work
| = | + | + | ||||
| 12 | 15 | 20 |
| = | = | = | ||||
| 60 | 60 | 5 |
∴ (A + B + C)’s 1 day’s work
| = | = | |||
| 5 × 2 | 10 |
∴ (A + B + C) together can complete the work in 10 days.
Now, A’s 1 day’s work
= (A + B + C)’s 1 day’s work –
(B + C)’s 1 day’s work
| = | - | = | = | |||||
| 10 | 15 | 30 | 30 |
∴ A alone can finish the work in 30 days.
Aliter : Using Rule 19,
Here, x = 12, y = 15, z = 20
A alone can do in
| = | xy + yz - zx |
| = | 12 × 15 + 15 × 20 - 20 × 12 |
| = | 180 + 300 - 240 |
| = | = 30 days | 240 |
