Question
Pipes A, B, and C can fill a tank in 30 minutes, 45
minutes, and 60 minutes respectively. All the pipes are opened together. A is closed after n minutes, and B is closed (2n - 2) minutes before the tank is filled. If the tank is filled in 28 minutes, find the value of n.Solution
Let the total capacity of tank be 180 litres (LCM of 30, 45, 60)
Efficiency of A = 180 ÷ 30 = 6 litres/minute
Efficiency of B = 180 ÷ 45 = 4 litres/minute
Efficiency of C = 180 ÷ 60 = 3 litres/minute So,
(6 + 4 + 3) × n + (4 + 3) × (28 - n - (2n - 2)) + 3 × (2n - 2) = 180
Or, 13n + 7(30 - 3n) + 6n - 6 = 180
Or, 13n + 210 - 21n + 6n - 6 = 180
Or, -2n + 204 = 180
Or, n = 12
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