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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.

A Q2 > Q1 > Q3 Correct Answer Incorrect Answer
B Q3 > Q2 < Q1 Correct Answer Incorrect Answer
C Q1 < Q2 < Q3 Correct Answer Incorrect Answer
D Q2 < Q3 > Q1 Correct Answer Incorrect Answer
E none of these Correct Answer Incorrect Answer

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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