Tap P can fill a cistern in 6 hours and tap Q can empty the full cistern in 10 hours. If both taps P and Q are kept open simultaneously, then in how many hours will the empty cistern be completely full ?

Explanation

Given: Tap P's 1 hour's work = 1/6 Tap Q's 1 hour's work = 1/10 Calculation: Tap(P + Q)'s 1 hour's work = 1/6 - 1/10 = 4/60 = 1/15 ∴ In 15 hours tank will be full. Shortcut Trick Time Work Efficiency P 6 5 30 Q 10 3 ⇒ (P + Q)'s combined efficiency = 5 - 3 = 2units/h ⇒ Time is taken to fill tank = 30/2 = 15 h