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?
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.