The question is from Pipes and Cisterns: Fill pipes and Drain Pipes. A question on possible values of fill pipes and drain pipes. How many fill and drain pipes required to fill the tank in 'x' hours? 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. Note: Some fill pipes and waste pipes amount to nothing. Between them they result in a net zero.
Question 1: A drain pipe can drain a tank in 12 hours, and a fill pipe can fill the same tank in 6 hours. A total of n pipes – which include a few fill pipes and the remaining drain pipes – can fill the entire tank in 2 hours. How many of the following values could ‘n’ take?
Two drain pipes can drain the same volume that one fill pipe fills. This means that a D-D-F combination has to have a net volume effect of 0.
In spite of this, the tank still gets filled. Only the fill pipes can manage to fill the tank. In addition to all the net zero effect pipes, we need three more fill pipes in order to fill the tank in 2 hours.
So, we can have as many D-D-Fs as we want, but we need one F-F-F at the end to ensure that the tank gets filled in 2 hours.
So the number of pipes will be → (D – D - F).......(D – D - F) + (F – F - F).
The number of pipes has to be a multiple of 3. Only options (a), (c) and (e) fit the description.
The question is "How many of the following values could ‘n’ take?"
Choice A is the correct answer.
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