Correct Option: C
| (A + B)’s 1 day’s work = | 1 | |
72 |
| (B + C)’s 1 day’s work = | 1 | |
120 |
| (C + A)’s 1 day’s work = | 1 | |
90 |
Adding all three,
| 2(A + B + C)’s 1 day’s work = | 1 | + | 1 | + | 1 |
72 | 120 | 90 |
| 2(A + B + C)’s 1 day’s work = | 5 + 3 + 4 | = | 12 | = | 1 |
360 | 360 | 30 |
| ∴ (A + B + C)’s 1 day’s work = | 1 | |
60 |
Now, A’s 1 day’s work = (A + B + C)’s 1 day’s work - (B + C)’s 1 day’s work
| A’s 1 day’s work = | 1 | - | 1 | |
60 | 120 |
| A’s 1 day’s work = | 2 - 1 | = | 1 | |
120 | 120 |
∴ A alone can complete the work in 120 days.
Second method to solve this question ,Here , x = 72 , y = 120 , z = 90
| A alone can do in = | 2xyz | |
xy + yz - zx |
| A alone can do in = | 2 × 72 × 120 × 90 | |
72 × 120 + 120 × 90 - 72 × 90 |
| A alone can do in = | 2 × 72 × 120 × 90 | |
8640 + 10800 – 6480 |
| A alone can do in = | 144 × 10800 | = 120 days |
12960 |
