Pipes and Cisterns - Aptitude Test Tricks, Formulas & Concepts

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.

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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

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

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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

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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 =

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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]

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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