A water cooler is filled when it is half empty with the help of a pipe which can fill the whole cooler in 50/3 minutes. There is an outlet tap at the bottom of the cooler which can empty the tank in 25 minutes. When the inlet pipe is started, a person comes and takes out the water from that tap for 1 minute then after a gap of 2 minutes another person comes and takes out the water for 1 minute and this process goes on. In how much time cooler will be completely full? Correct Answer 11 minutes Suppose the capacity of the tank = 50 units (LCM of 50/3 and 25) ∴ Efficiency of Inlet pipe = 50/(50/3) = 3 Efficiency of Outlet pipe = 50/25 = 2 Since the cooler is half empty ∴ Quantity of water to be filled = 50/2 = 25 units A person takes the water out for 1 minute and then 2 minute gap that means in 3 minutes, outlet tap is working for only 1 minute. After 9 minutes∶ Quantity of water filled = 3 × 9 – 2 × 3 = 21 units 10th minute∶ Both inlet and outlet will be working; ∴ Quantity of water filled = 3 – 2 = 1 unit 11th minute∶ Only inlet working; ∴ Quantity of water filled = 3 units ∴ Quantity of water filled upto 11 minutes = 21 + 1 + 3 = 25 units That means cooler is full in 11 minutes.