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
2. Framing equations for work time 2 concepts
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

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 = 4The correct answer is Choice (2).
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XAT TANCET Practice Questions  Listed Topic wise
 Number Theory
 Permutation Combination
 Probability
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 Geometry
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 Trigonometry
 Data Sufficiency
 Percentages
 Profit Loss
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 Mixtures & Alligation
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 Pipes, Cisterns & Work, Time
 Simple & Compound Interest
 Races
 Averages & Statistics
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 Set Theory
 Clocks Calendars
 Linear & Quadratic Equations
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