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P and Q can finish a work together in 30 hours. Q, R and S can finish the same work in 20 hours. And when all four of them work together, they finish the work in 15 hours. In how many hours can Q finish the work alone?

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P and Q can finish a work together in 30 hours. Q, R and S can finish the same work in 20 hours. And when all four of them work together, they finish the work in 15 hours. In how many hours can Q finish the work alone?


1). 40
2). 45
3). 60
4). 72


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3 vote
Answered by on | Votes 3 |

Let the efficiencies of P, Q, R and S be x, y, z and w.

P and Q can finish a work together in 30 hours. Q, R and S can finish the same work in 20 hours. And when all four of them work together, they finish the work in 15 hours.

⇒ x + y = 1/30

And, y + z + w = 1/20

And, x + y + z + w = 1/15

⇒ x = 1/15 – 1/20 = 1/60

⇒ y = 1/30 – x = 1/30 – 1/60 = 1/60

∴ Q can finish work alone in 60 hours.

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