Question
Three pipes A, B, and C can fill a tank in 50 minutes,
60 minutes, and 75 minutes respectively. All are opened together. A is closed after 'n' minutes, and B is closed (2n - 6) minutes before the tank is filled. If the tank is filled in 40 minutes, find the value of 'n'.Solution
Let the total capacity of tank be 300 litres (LCM of 50, 60, 75)
Efficiency of A = 300 ÷ 50 = 6 litres/minute
Efficiency of B = 300 ÷ 60 = 5 litres/minute
Efficiency of C = 300 ÷ 75 = 4 litres/minute So,
(6 + 5 + 4) × n + (5 + 4) × (40 - n - (2n - 6)) + 4 × (2n - 6) = 300
Or, 15n + 9(46 - 3n) + 8n - 24 = 300
Or, 15n + 414 - 27n + 8n - 24 = 300
Or, -4n + 390 = 300
Or, n = 22.5 minutes
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