The question is from Pipes and Cisterns: Two pipes. Two pipes filled a cistern and the details about their flow rate is given and we need to find out the time one of pipes was open. 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.

Question 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.

- 10 hrs
- 14 hrs
- 16 hrs
- 20 hrs

16 hrs

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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 = \\frac{475}{19}\\) = 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

The question is **"if the two pipes were open simultaneously the tank would fill in 19 hours."**

Choice C is the correct answer.

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