Three taps P,Q and R can individually fill a cistern in 7, 14 and 21 hours respectively .Tap P is opened first for 1 hour and then Tap P is closed and Tap Q is opened for 1hour, tap Q is then closed and Tap R is then opened for 1 hour after which Tap R is closed and Tap P opened again. This Process is continued till the tank is full. In how much time will the tank be completely full ?

Solution(By Examveda Team)

P can fill cister in7 hour.

Work rate of P = 100/7 = 14.28% per hour.

Q can fill the cistern in 14 hours.

Work Rate of Q = 100/14 = 7.14% per hour.

R can fill the cistern in 21 hours.

Work rate of R = 100/21 = 4.76% per hour.

Taking 3 hour = 1 unit of time.

In 1 unit of time, P, Q,R can fill = 14.28 + 7.14 + 4.76 = 26.28%.

In 3 unit of time day will fill = 26.28 *3 = 79% (approx.)

Rest cistern will be filled by  P and Q in next 2 hours.

Total Time taken = 3 Unit + 2 hour = 3 *3 + 2 = 11 hours.