Question
Pipes 'X' and 'Y' together can fill a tank in 30
minutes, while Pipe 'X' alone can fill the tank in 50 minutes. Another pipe 'Z' can empty the fully filled tank in 100 minutes. Find the time taken by pipes 'Y' and 'Z' together to fill 60% of the same tank.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.
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