CAT Practice : Pipes cisterns, Work time

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Classic Pipes - Cisterns Question!!

Pipes

    Q.17: A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours.
    1. 10 h
    2. 14 h
    3. 16 h
    4. 20 h

 

  • Correct Answer
    Choice C. 16 h

Detailed Solution

The 475 litres is filled in 19 hours by the two pipes when they are opened simultaneously.

Therefore, rate of water flow by A and B,

A + B = = 25 litres/hour………….(1)

Let pipe B was opened for t hours

Then, pipe A was opened for t + 5 hours

A x (t+5) + B x t = 475

(A + B) x t + 5A = 475

25t + 5A = 475

=) 5t + A = 95

Now, using option analysis

a) t = 10 =) 5 x 10 + A = 95 =) A = 45 (not possible from (1))

b) t = 14 =) 5 x 14 + A = 95 =) A = 25 (not possible from (1) as B can’t be zero)

c) t = 16 =) 5 x 16 + A = 95 =) A = 15

Correct Answer: 16 h



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Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.