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A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?
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- 80 days
- 100 days
- 60 days
- 150 days
Correct Option: C
| (A + B)’s 1 day’s work = | 72 |
| (B + C)’s 1 day’s work = | 120 |
| (C + A)’s 1 day’s work = | 90 |
On adding all three
| 2 (A + B + C)'s 1 days work = | + | + | 72 | 120 | 90 |
| 2 (A + B + C)'s 1 days work = | = | 360 | 30 |
| ∴ (A+B+C)’s 1 day’s work = | 60 |
∴ (A+B+C) will do the work in 60 days.
Second method to solve this question ,
Here , x = 72 , y = 120 , z = 90
| Time taken = | xy + yz + zx |
| Time taken = | 72 × 120 +120 × 90 +72 × 90 |
| = | 8640 + 10800 + 6480 |
| = | = 60 days | 25920 |
