Question
Three pipes A, B, and C can fill a tank in 24 minutes,
36 minutes, and 48 minutes respectively. All are opened together. A is closed after 'n' minutes, and B is closed (2n - 4) minutes before the tank is filled. If the tank is filled in 20 minutes, find the value of 'n'.Solution
Let the total capacity of tank be 144 litres (LCM of 24, 36, 48)
Efficiency of A = 144 ÷ 24 = 6 litres/minute
Efficiency of B = 144 ÷ 36 = 4 litres/minute
Efficiency of C = 144 ÷ 48 = 3 litres/minute So,
(6 + 4 + 3) × n + (4 + 3) × (20 - n - (2n - 4)) + 3 × (2n - 4) = 144
Or, 13n + 7(24 - 3n) + 6n - 12 = 144
Or, 13n + 168 - 21n + 6n - 12 = 144
Or, -2n + 156 = 144
Or, n = 6
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