Pipes & Cistern Practice Question

This aptitude practice question helps understand the basics of how problems in pipes and cisterns should be solved. The rate at which a pipe fills a tank is usually provided in terms of the time taken by a pipe to fill the tank. Therefore, the rate at which it fills is computed as a fraction of the tank that gets filled in unit time. These questions are commonly classified as word problems in GMAT and GRE as solving these questions entail framing mathematical expressions and equations from information given in words. An easy to medium level difficulty question.

Question

Medium Quant

A tank is fitted with 8 pipes, some of which that fill the tank and others that empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of those that empty the tank empties it in 6 hours. If all the pipes are kept open when the tank is full, it will take 6 hours to drain the tank. How many of these are fill pipes?

2 fill pipes
4 fill pipes
6 fill pipes
5 fill pipes

Correct Answer Choice (2). 4 of the 8 pipes are fill pipes .

Explanatory Answer

Step 1 Step 2 Tabs

Words to Mathematical Expressions and Equations

Let the number of fill pipes be 'n'
Therefore, there will be (8 - n) waste pipes.

Each of the fill pipes can fill the tank in 8 hours.
Therefore, each of the fill pipes will fill \\frac{1}{8}\\)th of the tank in an hour.

Hence, n fill pipes will fill \\frac{n}{8}\\)th of the tank in an hour.

Similarly, each of the waste pipes will drain the full tank in 6 hours.
∴ each of the waste pipes will drain \\frac{1}{6}\\)th of the tank in an hour.

(8 - n) waste pipes will drain \\frac{(8 - n)}{6}\\)th of the tank in an hour.
Solve the equation to get the answer

Between the fill pipes and the waste pipes, they drain the tank in 6 hours.
That is, when all 8 of them are opened, \\frac{1}{6}\\)th of the tank gets drained in an hour.

(Amount of water filled by fill pipes in 1 hour - Amount of water drained by waste pipes 1 hour) = \\frac{1}{6}\\)th of the tank

\\frac{n}{8}\\) - \\frac{(8 - n)}{6}\\) = \\frac{-1}{6}\\)
Note: The right hand side has a negative sign because the tank gets drained.

Cross multiplying and solving the equations, 14n - 64 = -8
Or 14n = 56 or n = 4

The correct answer is Choice (2).