Question
Pipe Q and Pipe R together can fill a tank in 25
minutes. With Pipe S, all three pipes can fill the tank in 30 minutes. Pipe Q and Pipe T together can fill the tank in 30 minutes. Pipe S and Pipe T together can fill the tank in 75 minutes. Pipe R, Pipe S and Pipe U together can fill the tank in 75/4 minutes. Quantity I : Pipe R is opened for 15 minutes and then closed. Find the time taken by Pipe T to fill the remaining part of the tank.Ā Quantity II : Pipe Q is opened for 10 minutes and then closed. Find the time taken by Pipe S to empty the filled part of the tank. Quantity IIIĀ : Find the time taken by Pipe Q, Pipe S and Pipe U to fill the tank.Solution
letĀ Q + R = 256Ā ThenĀ Ā Q + R + T = 305Ā Q + T = 30 } 150 { 5Ā Ā S + T = 75 2Ā R + S + U = 18.75 8Ā Ā S = 5 ā 6 = ā 1, T = 2 ā ( ā 1) = 3, Q = 5 ā 3 = 2, R = 6 ā 2 = 4,Ā Ā T = 8 ā 4 ā ( ā 1) = 5Ā So, Time taken by T to fill remaining tank = (150 ā 15 Ć 4)/3 =Ā 50 ā 20 = 30 minute = Q1 LetĀ Time taken by S to empty the filled part of tank = (10 Ć 2)/1 = 20 minute = Q2 ThereforeĀ Time taken by Q, S & U to fill the tank = 150/(2 ā 1 + 5)Ā = 150/6 = 25 minute = Q3
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