# How To Solve Pipes & Cisterns Questions Quickly

## How to solve Pipe cistern questions quickly

A cistern or tank  is connected to a pipe . The Pipe is used to fill the cistern known as Inlet and the Pipe which is used to empty the tank known as Outlet;

### 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 $\frac{8}{11}$ mins

Solution:    Part of the tank filled by pipe A = $\frac{1}{5}$

Part of the tank filled by pipe B = $\frac{1}{6}$

Together they take = $\frac{1}{5}$ + $\frac{1}{6}$ = $\frac{11}{30}$

Therefore, pipes A and B can fill the tank in $\frac{30}{11}$ hours

Correct option: D

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 = $\frac{1}{x}$+ $\frac{1}{x+5}$ = $\frac{1}{6}$

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.

Correct option: A

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 $\frac{a}{2}$ and $\frac{a}{4}$ respectively

Now together they takes 5 hours

Therefore $\frac{1}{x}$ + $\frac{2}{x}$ + $\frac{4}{x}$ = $\frac{1}{6}$
$\frac{7}{x}$ = $\frac{1}{6}$

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 = $\frac{1}{5}$

Now, due to leakage in pipe, filled part in 1 hour = 1/10

Part of the cistern emptied, due to leakage in 1 hour = $\frac{1}{5}$$\frac{1}{10}$ = $\frac{1}{10}$

Therefore the leak pipe will empty the cistern in 10 hrs.

Correct option: A

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 $\frac{7}{3}$ 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 = $\frac{1}{2}$$\frac{3}{7}$ = $\frac{1}{14}$

It means leak will empty the vessel in 14 hrs.

Correct option: D

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 = $\frac{1}{12}$+$\frac{1}{20}$=$\frac{2}{15}$

Therefore both rivers filled the dam in $\frac{15}{2}$ hrs.

Now, due to leakage both rivers filled the dam in $\frac{15}{2}$ + $\frac{30 min}{60 min}$ = 8hrs.

Due to leakage, part filled in one hour = $\frac{1}{8}$

Therefore, part of dam emptied, due to leakage in one hour = $\frac{2}{15}$$\frac{1}{28}$= $\frac{1}{120}$

Therefore, in 120 hrs, the leak would empty the dam.

Correct option: D

### 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 * ($\frac{1}{10}$ + $\frac{1}{15}$) = 2 * $\frac{5}{30}$= $\frac{5}{15}$

Remaining part = (1-$\frac{1}{3}$) = $\frac{2}{3}$

Now, part filled by tap T2 = $\frac{1}{20}$

Therefore, $\frac{1}{20}$: $\frac{1}{3}$:: 1 : x

On solving we get x = $\frac{40}{3}$ (13 min 20 sec)

Therefore, the bucket will be filled in = 2 minutes + 13 minutes + 20seconds = 15 min and 20 sec

Correct option: B

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. $\frac{105}{41}$hrs

B. 41 hrs

C. $\frac{134}{43}$ hrs

D. $\frac{122}{13}$ 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 $\frac{1}{3}$ th and $\frac{1}{5}$th part of the pond in 1 hour respectively.

Part of the pond emptied in 1 hour by pipe P3 = $\frac{1}{7}$

Therefore, in 1 hour part of the pond filled is = ($\frac{1}{3}$ + $\frac{1}{5}$$\frac{1}{7}$) = $\frac{41}{105}$

Therefore, tank will be filled completely in $\frac{105}{41}$ hrs

Correct option: A

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. $\frac{321}{47}$ min

B. $\frac{311}{47}$ min

C. $\frac{1621}{47}$ min

D. $\frac{321}{22}$ min

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

$\frac{x}{12}$ + $\frac{x – 2 }{16}$ + $\frac{x – 4 }{20}$ = 1

x = $\frac{162}{47}$ = $\frac{321}{47}$ min

Correct option: A