Question
Pipes 'X' and 'Y' can fill a tank in 30 minutes and 45
minutes respectively. Both are opened together. After the tank is half full, a leak develops which drains (1/3)rd of the incoming water. Find the total time taken to fill the tank.Solution
Let the tank capacity be 90 litres (LCM of 30 and 45)
Efficiency of 'X' = 90 ÷ 30 = 3 litres/min
Efficiency of 'Y' = 90 ÷ 45 = 2 litres/min
Time to fill half = (0.5 × 90) ÷ (3 + 2) = 45 ÷ 5 = 9 minutes
Effective rate after leak = (2/3) × (3 + 2) = 10/3 litres/min
Time to fill remaining = 45 ÷ (10/3) = 13.5 minutes
Total time = 9 + 13.5 = 22.5 minutes
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