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Two workers A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work than when work together. If B worked alone, would take
4 1 hours more than 2
when work together. The time required to finish the work together is
-
- 5 hours
- 4 hours
- 8 hours
- 6 hours
Correct Option: D
Time taken by A and B = x hours (let).
∴ According to the question,
Time taken by A alone = (x + 8) hours.
Time taken by B alone
| = |  | x + |  | hours. | 2 |
| ∴ | + | = | ||||
| x + 8 | x + (9/2) | x |
| ∴ | + | = | ||||
| x + 8 | 2x + 9 | x |
| = | = | |||
| (x + 8)(2x + 9) | x |
| = | = | |||
| 2x2 + 16x + 9x +72 | x |
&rArrr; 4x2 + 25x = 2x2 + 25x + 72
⇒ 2x2 = 72
| ⇒ x2 = | = 36 | 2 |
⇒ x =√36 = 6 hours
