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. 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 III : Find the time taken by Pipe Q, Pipe S and Pipe U to fill the tank.
Solution
let Q + R = 256 Then  Q + R + T = 305 Q + T = 30 } 150 { 5  S + T = 75 2 R + S + U = 18.75 8  S = 5 – 6 = – 1, T = 2 – ( – 1) = 3, Q = 5 – 3 = 2, R = 6 – 2 = 4,  T = 8 – 4 – ( – 1) = 5 So, Time taken by T to fill remaining tank = (150 – 15 × 4)/3 = 50 – 20 = 30 minute = Q1 Let Time taken by S to empty the filled part of tank = (10 × 2)/1 = 20 minute = Q2 Therefore Time taken by Q, S & U to fill the tank = 150/(2 – 1 + 5) = 150/6 = 25 minute = Q3
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