# Pipes and Cisterns - Aptitude Test Tricks, Formulas & Concepts

Quantitative aptitude questions on pipes and cisterns are similar to time and work problems. They are commonly asked questions for bank tests, career recruitment tests, management entrance tests and other competitive exams. Questions on pipes and cisterns can be mixed with questions on mixtures and alligations to increase the difficulty level of questions. Quantitative aptitude questions on pipes and cisterns when mixed with ratios can be a bit tricky. But a strong understanding of the concept behind solving them and practicing as much questions as possible can help you easily solve them.

In this paper we will have a look at frequently asked top aptitude questions on pipes and cisterns, basic concepts, important formulas and tricks and shortcuts on how to solve pipes and cisterns problems easily and quickly.

Frequently asked aptitude questions on pipes and cisterns include:
1. Given time taken by individual pipes to empty/fill up a tank. How much does it take to fill / empty the tank if they work together.
2. Given time taken by the each pipe to fill up a tank if they work alone. Also given rate in Liters/minute at which an outlet pipe can empty the tank. Find the capacity of the tank.
3. Given time taken by the each pipe to fill up a tank if they work alone. After some time t min one of the pipes is closed and given tank is filled up in x hours. Find time t.
4. Given time taken by the each pipe to fill up a tank if they work alone. Both the pipes are opened together and given after t minutes, a pipe is turned off. What is the total time required to fill the tank.
5. Given a pipe can fill a tank in x hrs. Because of a leak at the bottom of tank, it takes y hrs to fill up the tank. If the tank is full, how much time will it take to empty the full tank.
6. Given a pipe can fill the tank n times faster than another pipe. Given the time taken by them to fill up the tank when they work together. Find the time taken by them to fill up the empty tank if they function individually.
7. Given time taken by each pipe to fill up an empty tank if they function separately. One of the pipes is full time functioning while 2 other pipes are open for one hour each alternately. Then find the amount of time taken to fill up the empty tank.

## Core Concepts

1. A pipe which fills up the tank is known as inlet.
2. A pipe which empties the tank is known as outlet.
3. A pipe takes x hours to fill up the tank. Then 1/x parts of the tank will be filled in 1 hour.
4. A pipe takes y hours to empty the tank. Then part emptied in 1 hour = 1/y
5. Pipe A can fill a tank n times as fast as another pipe B. This means: If slower pipe B takes x min to fill up the empty tank,
then faster pipe A takes x/n min to fill up the empty tank. If they operate together, then part of the tank that is filled up in 1 hour is (n + 1)/x
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## Important Formulas, Shortcuts with Explanation

Scenario 1: A tank has 2 inlet pipes A and B. Pipe A alone can fill up the tank in a hrs. Pipe B alone can fill up the tank in b hrs. How much time will it take to fill up the tank, if both pipes are opened together?

Let V be the volume of tank.
Pipe A can fill V/a parts of tank in 1hr.
Pipe B can fill V/b parts of tank in 1 hr.
If both pipes function together, let c hrs be the time taken to fill up tank.
That means, V/c parts of tank will be filled in 1 hr.
ie; V/a + V/b parts of tank will be filled in 1 hr.
V/a + V/b = V/c

c = ab/(a+b) hrs

Scenario 2: An inlet pipe takes x hours to fill up the tank. An outlet pipe takes y hours to empty the tank. Then if both pipes are opened

1. If y > x, net part filled up in 1 hr = 1/x – 1/y
2. If x > y, net part emptied in 1 hr = 1/y – 1/x

Scenario 3: If there are n pipes to a tank which takes p1, p2, p3, p4, .. pn hours to fill up the tank, when operating alone. Then if all pipes are opened together:

Part of the tank that is filled up in 1 hr =
Time taken to fill up the tank =

Scenario 4: If there are n pipes to a tank which takes p1, p2, p3,p4, .. pn hours to fill up the tank, when operating alone. The tank also has an outlet pipe which takes p0 hours to empty the tank. Then if all pipes are opened together:

Part of the tank that is filled up in 1 hr = [ -ve sign implies emptying the tank]

Scenario 5: A pipe can fill a tank in x hrs. Because of a leak at the bottom of tank, it takes y hrs to fill up the tank. If the tank is full, how much time will it take to empty the full tank?

Time take to empty the tank = xy / (y – x) hours

Practice Makes Perfect

Last but not the least, practice as many question as you can to gain better understanding of these formulas and to improve your speed in solving them. Here is a sample set of solved quantitative aptitude questions based on pipes and cisterns. Take the test and strengthen your understanding.