Question
Time taken by pipes 'X', 'Y' and 'Z' to fill a tank is
48 minutes, 80 minutes and 60 minutes respectively. All the pipes are opened together. 'X' is closed after 't' minutes, and 'Y' is closed (2t - 1) minutes before the tank is filled. If the tank is filled in 35 minutes, then determine the value of 't'.Solution
ATQ, Let the total capacity of tank be 240 litres (LCM of 48, 60 and 80) Efficiency of 'X' = (240/48) = 5 litres/minute Efficiency of 'Y' = (240/80) = 3 litres/minute Efficiency of 'Z = (240/60) = 4 litres/minutes So, (5 + 3 + 4) × t + (3 + 4) × (35 - t - 2t + 1) + 4 × (2t - 1) = 240 Or, 12t + 252 - 21t + 8t - 4 = 240 Or, 't' = 8
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