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Three men A. B and C working together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in
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2 hour. 3 -
2 hour. 4 -
3 hour. 2 -
4 hour. 3
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Correct Option: D
Let A, B and C together do the work in t hours.
∴ Time taken by A = (d + 6) hours
Time taken by B = (t + 1) hours
Time taken by C = 2t hours
| ∴ | + | + | = | t + 6 | t + 1 | 2t | t |
| ⇒ | + | = | - | t + 6 | t + 1 | t | 2t |
| = | ||
| 2t |
| ⇒ | = | - | t + 6 | 2t | t + 1 |
| = | ||
| 2t(t + 1) |
| = | = | t + 6 | 2t2 + 2t |
⇒ 2t2 + 2t = t + 6 – t2 – 6t
⇒ 3t2 + 7t – 6 = 0
⇒ 3t2 + 9t – 2t – 6 = 0
⇒ 3t (t + 3) – 2 (t + 3) = 0
⇒ (3t – 2) (t +3) = 0
⇒ 3t – 2 = 0 as t + 3 ≠ 0
| ⇒ t = | ||
| 3 |
| ∴ Time taken by A = 6 + | ||
| 3 |
| = | = | hours | 3 | 3 |
| Time taken by B = 1 + | ||
| 3 |
| = | hours | |
| 3 |
∴ (A +B)’s 1 hour’s work
| = | + | 20 | 5 |
| = | ||
| 20 |
| = | = | 20 | 4 |
| ∴ Required time = | hours | |
| 3 |
