-
A and B can do a piece of work in 15 days. B and C can do a similar work in 12 days and C and A in 10 days. How many days will A take to do the work by himself ?
-
- 13
- 24
- 40
- 8
Correct Option: B
(A + B)’s 1 day’s work
| ..........(i) | 15 |
(B + C)’s 1 day’s work
| ..........(ii) | 12 |
(C + A)’s 1 day’s work
| ..........(iii) | 10 |
On adding all three equations,
2 (A + B + C)’s 1 day’s work
| = | + | + | ||||
| 15 | 12 | 10 |
| = | = | = | ||||
| 60 | 60 | 4 |
∴ (A + B + C)’s 1 day’s work
| ..........(iv) | 8 |
By equation (iv) – (ii),
A’s 1 day’s work
| - | ||||
| 8 | 12 |
| = | ||||
| 24 | 24 |
∴ Required time = 24 days
Aliter : Using Rule 19,
| A alone can do in = | xy + yz - zx |
| = | 15 × 12 + 12 × 10 - 10 × 15 |
| = | 36 + 24 - 30 |
| = | 24 days | 60 - 30 |
