Correct Option: B
| (A + B)’s 1 day’s work = | 1 | |
| 36 |
| (B + C)’s 1 day’s work = | 1 | |
| 60 |
| (C + A)’s 1 day’s work = | 1 | |
| 45 |
Adding all three,
| 2(A + B + C)’s 1 day’s work = | 1 | + | 1 | + | 1 |
36 | 60 | 45 |
| 2(A + B + C)’s 1 day’s work = | 5 + 3 +4 | = | 1 | |
180 | 15 |
| ∴ (A + B + C)’s 1 day’s work = | 1 | |
| 30 |
| ∴ C’s 1 day’s work = | 1 | - | 1 | |
30 | 36 |
| C’s 1 day’s work = | 6 - 5 | | 1 | |
180 | 180 |
Hence, C alone will finish the work in 180 days.
Second method to solve this question ,Here , x = 36 , y = 60 , z = 45
| C alone can do in = | 2xyz | |
| xy - yz + zx |
| C alone can do in = | 2 × 36 × 60 × 45 | |
| 36 × 60 - 60 × 45 + 45 × 36 |
| C alone can do in = | 2 × 36 × 60 × 3 | |
| 144 - 180 + 108 |
| C alone can do in = | 72 × 180 | = 180 days |
| 252 - 180 |
