# How To Solve Pipes & Cisterns Quickly

## How to Solve Quickly Pipes And Cisterns questions

A pipe is connected to a tank or cistern to fill or empty the tank or cistern
Inlet: A pipe which is connected to fill a tank is known as an inlet.
Outlet: A pipe which is connected to empty a tank is known as an outlet.

## Type 1: Calculate time taken to fill a tank by two or more pipes

### Question 1.

Two pipes A and B can fill a tank in 5 and 6 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

Options:
A. 3 hrs and 11 mins
B. 30 hrs and 10 mins
C. 3 hrs and 10 mins
D. 2 hrs and 8/11 mins

#### Solution:

Part of the tank filled by pipe A = 1/5
Part of the tank filled by pipe B = 1/6
Together they take = 1/5 + 1/6 = 11/30
Therefore, pipes A and B can fill the tank in 30/11 hours

### Question 2.

There are two pipe A and B connected to a tank. The tank can be filled in 6 minutes, if pipe A takes 5 minutes less than pipe B, How much time will pipe B take if it is alone filling the tank.

Options:
A. 15 min
B. 12 min
C. 10 min
D. 5 min

#### Solution:

Time taken by Pipe A to fill the tank = x minutes
Therefore, pipe B will fill the bucket in (x+5) minutes.
Now, when both the pipes are filling the tank = 1/x + 1/(x+5) = 1/6
On solving we get, x = 10
So, pipe A can fill in 10 minutes and pipe B can fill the bucket in (x+5)= 10+ 5 =15 mins.

### Question 3.

Three Pipes P1, P2, P3 can fill a swimming pool in 6 hours. The pipe P3 is twice as fast as P2 and P2 is twice as fast as P1. Find out how much time will pipe P1 alone take to fill the swimming pool?

Options:
A. 35 hrs
B. 42 hrs
C. 24 hrs
D. 38 hrs

#### Solution:

Let the Pipe P1 take ‘a’ hours to fill the swimming pool
It means P2 and P3 will take a/2 and a/4 respectively
Now together they takes 5 hours
Therefore 1/x + 2/x + 4/x = 1/6
7/x = 1/6
x = 42 hrs.
Therefore, a will take 42 hours

#### Correct option: B ## Type 2: Calculate time taken to fill a tank having a hole or leakage

### Question 1.

A cistern takes 5 hrs to be filled by pipe. But there is one leakage in the pipe due to which it takes 10 hrs. Find out how much time will the leakage pipe to empty the cistern?
Options:
A. 10 hrs
B. 10 min
C. 20 hrs
D. 20 min

#### Solution:

Cistern is filled in 5 hours,
Therefore in 1 hour part filled is = 1/5
Now, due to leakage in pipe, filled part in 1 hour = 1/10
Part of the cistern emptied, due to leakage in 1 hour = 1/5 – 1/10 = 1/10
Therefore the leak pipe will empty the cistern in 10 hrs.

### Question 2.

A pipe can fill a vessel with milk in two hours. But there was a leakage in the pipe which made it took 7/3 hours to fill the vessel with milk. The leak can drain all the milk of the vessel in how much time?
Options:
A. 10 hrs
B. 11 hrs
C. 7 hrs
D. 14 hrs

#### Solution:

Due to leak the vessel filled in one hour = 1/2- 3/7 = 1/14
It means leak will empty the vessel in 14 hrs.

### Question 3.

There are two rivers R1 and R2. Both the rivers can fill a dam in 12 and 20 hours respectively. The rivers are opened simultaneously. An engineer found that there is a hole in the dam due to which half hour extra is taken for the dam to be filled up completely. If the dam is completely full then in what time will the leak empty it?
Options:

A. 100 hrs
B. 110 hrs
C. 107 hrs
D. 120 hrs

#### Solution:

Dam filled by both rivers in one hour = 1/12+1/20=2/15
Therefore both rivers filled the dam in 15/2hrs.
Now, due to leakage both rivers filled the dam in 15/2 + 30min / 60min = 8hrs.
Due to leakage, part filled in one hour = 1/8
Therefore, part of dam emptied, due to leakage in one hour = 2/15 – 1/8 = 1/120
Therefore, in 120 hrs, the leak would empty the dam.

## Type 3: Calculate Time Taken When Pipes Are Opened For Different Periods

### Question 1:

Two taps T1 and T2 can fill a bucket in 10 minutes and 15 minutes. Both the taps are opened together. However, after 2 minutes, tap T1 is closed. What is the total time required to fill the bucket?

Options:
A. 11 min and 20 sec
B. 15 min and 20 sec
C. 13 min and 40 sec
D. 15 min and 40 sec

#### Solution:

Part filled in 2 min = 2 * (1/10 + 1/ 15) = 2 * 5/30 = 5/15
Remaining part = (1-1/3) = 2/3
Now, part filled by tap T2 = 1/20
Therefore, 1/20 : 1/ 3:: 1 : x
On solving we get x = 40/3 (13 min 20 sec)
Therefore, the bucket will be filled in = 2 minutes + 13 minutes + 20seconds = 15 min and 20 sec

### Question 2.

A pond can be filled by two pipes P1 and P2. P1 takes 3 hours and P2 takes 5 hours. There is another pipe P3 attached to the pond which can empty the pond in 7 hours. If all the pipes are opened at the same time then in how much time will the empty pond be fully filled?
Options:

A. 105/41 hrs
B. 41 hrs
C. 134/43 hrs
D. 122/13 hrs

#### Solution:

Time taken by Pipe P1 to fill the tank = 3 hr
Time taken by pipe P2 to fill the tank = 5 hr
Time taken by pipe P3 to empty the tank = 7 hr
Therefore, pipe P1 and P2 fills 1/3 th and 1/5th part of the pond in 1 hour respectively.
Part of the pond emptied in 1 hour by pipe P3 = 1/7
Therefore, in 1 hour part of the pond filled is = (1/3 + 1/5 – 1/7) = 41/105
Therefore, tank will be filled completely in 105/41 hrs

### Question 3.

Pipe M takes 12, pipe N takes 16, and Pipe O takes 20 minutes to fill a water container. Pipe M was opened first. After 2 minute, pipe N was opened. After 2 minutes from the start of N, pipe O was also opened. Find the time when water container will be full after opening of pipe O?
Options:

A. 321/47min
B. 311/47min
C. 1621/47min
D. 321/22min

#### Solution:

Let water container get full in x min.
Then part filled by pipe M in x min + part filled by pipe N in (x-2) min + part filled by pipe O in (x-4) min = 1
x/12 + (x-2)/16 + (x-4)/20 = 1
x = 162/47 = 321/47min