A pipe P,can fill an empty tank in 12 min and another pipe Q, can empty same tank in 20 min. Pipe P is configured to close automatically when the water level reaches in the tank reaches 3/4th of the height of the tank and simultaneously the pipe Q opens and operates until the water level fall to exactly 1/4th of the height of the tank after which it closes and simultaneously P opens. If this process continues indefinitely, what portion of the tank is filled after exactly one hour?(assume that tank is initially empty)

9 mins for P to fill 3/4th tank and then 10 mins to Q to empty it till 1/4th.thus after 19 min-1/4.

then 6 min for P to reach 3/4th and 10 min for Q to take it to 1/4th.Thus 16 min.

so after 19+2*16=51 mins,it will be at 1/4th and then P fill it till 57th min and then in 3 min Q empty it by 3/20th so final answer: 3/4-3/20=12/20=3/5

A pump can be used for filling as well as for emptying a tank. The capacity of the tank is 1500 m^{3}. The emptying capacity of the tank is 10 m^{3}^{ }per minute higher than its filling capacity and the pump needs 5 minutes lesser to empty the tank than it needs to fill it. What is the emptying capacity of the pump?

Suppose the filling capacity of the tank = x m^{3} per min

so, 1500/x – 1500/( x+ 10) = 5

x^{2} + 10x – 3000 = 0

Solving this we get x = 50

Emptying capacity : 50 + 10 => 60 m^{3} per min.

Two taps are running continuously to fill a tank. The 1st tap could have filled it in 5hrs by itself and second can fill it in 20 hours . But the operator failed to realise that there was a leak in the tank from begining which caused a delay of one hour in the filling of the tank. Find the time in which the leak would empty a filled tank.

A 15

B 20

C 25

D 40