Correct Option: D
| (A + B)'s 1 day's work = | 1 | .....(i) |
12 |
| (B + C)'s 1 day's work = | 1 | .....(ii) |
8 |
| (C + A)'s 1 day's work = | 1 | .....(iii) |
6 |
On adding,
| 2(A + B + C)'s 1 day's work = | 1 | + | 1 | + | 1 |
12 | 8 | 6 |
| 2(A + B + C)'s 1 day's work = | 2 + 3 + 4 | = | 9 | |
24 | 24 |
| ∴ (A+ B + C)'s 1 day’s work = | 9 | = | 9 | .....(iv) |
24 × 2 | 48 |
On, subtracting (iii) from (iv),
| B’s 1 day’s work = | 9 - 8 | = | 1 | |
48 | 48 |
∴ B can complete the work in 48 days.
Second method to solve this question ,Here , x = 12 , y = 8 , z = 6
| Time taken = | 2xyz | |
- xy + yz + zx |
| B alone can do in = | 2 × 12 × 8 × 6 | |
- 12 × 8 + 8 × 6 + 6 × 12 |
| Time taken = | 24 × 48 | |
- 96 + 48 + 72 |
| Time taken = | 24 × 48 | |
- 96 + 120 |
| Time taken = | 24 × 48 | = 48 days. |
24 |
