Pipe 'A' alone can fill 80% of a tank in 32 minutes and pipe 'C' is 60% more efficient than pipe 'A'. Pipes 'A', 'B' and 'C' together take 24 minutes to fill the same tank. If the tank develops a leak that can empty the fully filled tank in 5 hours, then find the time taken by pipes 'B' and 'C' together (along with leak) to fill half of the same tank, now.

Time taken by pipe 'A' alone to fill the entire tank = 32 ÷ 0.8 = 40 minutes So, time taken by pipe 'C' alone to fill the entire tank = 40 ÷ 1.6 = 25 minutes Let the total capacity of the tank = L.C.M of 40, 25 and 24 = 600 units So, efficiency of pipe 'A' alone = (600/40) = 15 units/minute Efficiency of pipe 'C' alone = (600/25) = 24 units/minute Combined efficiency of pipes 'A', 'B' and 'C' = (600/24) = 25 units/minute So, efficiency of pipe 'B' alone = 25 - 15 - 24 = -14 units/minute {Negative sign shows that pipe 'B' is an outlet pipe} Efficiency of the leak = 600 ÷ (5 X 60) = 2 units/minute Combined efficiency of pipes 'B' and 'C' with the leak = (24 - 14) - 2 = 8 units/minute Capacity of half of the tank = (600/2) = 300 units So, time taken by pipes 'B' and 'C' together to fill half of the tank (with leak) = (300/8) = 37.5 minutes