Pipes 'X' and 'Y' together can fill a tank in 30

Solution

Let the total capacity of the tank be 150 litres (LCM of 30, 50, and 100). Combined efficiency of 'X' and 'Y' = (150 / 30) = 5 litres/minute. Efficiency of 'X' = (150 / 50) = 3 litres/minute. So, efficiency of 'Y' = 5 - 3 = 2 litres/minute. Efficiency of 'Z' = (150 / 100) = -1.5 litres/minute (negative sign shows outlet pipe). Capacity of tank to be filled = 0.6 × 150 = 90 litres. So, required time = 90 ÷ (2 - 1.5) = 90 ÷ 0.5 = 180 minutes.