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A can do as much work as B and C together can do. A and B can together do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is :
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- 18 hrs
- 24 hrs
- 30 hrs
- 12 hrs
Correct Option: B
| 9 hours 36 minutes = 9 + | = 9 | hours | 60 | 5 |
| 9 hours 36 minutes = | hours | |
| 5 |
| (A + B)’s 1 hour’s work = | ||
| 48 |
| C’s 1 hour’s work = | ||
| 48 |
| (A + B + C)’s 1 hour’s work = | + | = | .......(i) | 48 | 48 | 8 |
A’s 1 hours work = (B + C)’s 1 hour’s work .....(ii)
From equations (i) and (ii),
| 2 × (A’s 1 hour’s work) = | ||
| 8 |
| A’s 1 hour’s work = | ||
| 16 |
| ∴ B’s 1 hour’s work = | - | 48 | 16 |
| B’s 1 hour’s work = | = | 48 | 24 |
∴ B alone will finish the work in 24 hours
