Arithmetic aptitude :: Pipes and Cisterns :: Solved Examples

• Pipes and Cisterns - Solved Examples
• Pipes and Cisterns - Data Sufficiency 1
• Pipes and Cisterns - Data Sufficiency 2
• Pipes and Cisterns - Important Formulas and Facts

1. Inlet:

An Inlet is a pipe which is connected with a tank or cistern or reservoir, which fills it.

2. Outlet:

 An Outlet is a pipe which is connected with a tank or cistern or reservoir, which empties it.

3. If an inlet can fill a tank in $x$ hours, then, part filled in $1$ hour $=\frac{1}{x}$.

4. If an outlet can empty a tank in $y$ hours, then: part emptied in $1$ hour $=\frac{1}{y}$.

5. If a pipe $A$ can fill a cistern in $x$ hours and another pipe $B$ can empty the full tank in $y$ hours (where $y>x$), then on opening both

the pipes, then, the net part filled in $1$ hour $=\left(\frac{1}{x}-\frac{1}{y}\right)$.

6. If an inlet can fill a reservoir in $x$ hours and another outlet can empty the full tank in $y$ hours (where $x>y$), then on opening both

inlet and outlet, then, the net part emptied in $1$ hour $=\left(\frac{1}{y}-\frac{1}{x}\right)$.

A pump can fill a tank with water in $2$ hours. Because of a leak, it took $2\frac{1}{3}$ hours to fill the tank. The leak can drain all the water of the tank in :

Answer:

Explanation:

Work done  by the leak in $1$ hour $=\left(\frac{1}{2}-\frac{3}{7}\right)$  $=\frac{1}{14}$.

$\therefore$ Leak will empty the tank in 14 hours.

A water tank is $\frac{2}{5}$ full. Pipe $A$ can fill a tank in $10$ minutes and pipe $B$ can empty it in $6$ minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

Answer:

Explanation:

Clearly, pipe $B$ is faster than pipe $A$ and so, the tank will be emptied.

Part to be emptied  $=\frac{2}{5}$.

Part emptied by  $(A+B)$ in $1$ minute  $=\left(\frac{1}{6}-\frac{1}{10}\right)$  $=\frac{1}{15}$.

$\therefore$ $\frac{1}{15}:\frac{2}{5}::1:x$ or  $x=\left(\frac{2}{5}\times 1\times 15\right)$  $=6$ min.

So, the tank will be emptied in 6 min.

Two pipes A and B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minutes ?

Answer:

Explanation:

Let $B$ be closed after $x$ minutes. Then,

part filled by $(A+B)$ in $x$ min + part filled by $A$ in $(18-x)$ min $= 1$

$\Leftrightarrow x\left( \frac{1}{24}+\frac{1}{32}\right)+\left(18-x\right) \times\frac{1}{24}=1$

$\Leftrightarrow\frac{7x}{96}+\frac{18-x}{24}=1$

$\Leftrightarrow 7x+4(18-x)$ $=96$

$\Leftrightarrow 3x=24$ $\Leftrightarrow x=8$

Hence, $B$ must be closed after 8 minutes.

Two pipes $A$ and $B$ can fill a tank in $36$ min and $45$ min respectively. A water pipe $C$ can empty the tank in $30$ min. First $A$ and $B$ are opened. After $7$ minutes, $C$ is also opened. In how much time, the tank is full ?

Answer:

Explanation:

Part filled in $7$ min $=7\left( \frac{1}{36}+\frac{1}{45}\right)$ $=\frac{7}{20}$

Remaining part $=\left( 1- \frac{7}{20}\right)$ $=\frac{13}{20}$

Net part filled in $1$ min. when $A$, $B$ and $C$ are opened $=\left(\frac{1}{36}+\frac{1}{45}-\frac{1}{30}\right)$ $=\frac{1}{60}$

Now, $\frac{1}{60}$ part is filled in $1$ min.

$\frac{13}{20}$ part is filled in $\left(60\times\frac{13}{20}\right)$ $=39$ min

Total time taken to fill the tank $=(39+7)$ min = 46 min.

Two pipes can fill a cistern in $14$ hours and $16$ hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took $32$ minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it ?

Answer:

Explanation:

Work done by the two pipes in $1$ hour $=\left(\frac{1}{14}+\frac{1}{16} \right)$ $=\frac{15}{112}$

Time taken by these pipes to fill the tank $=\frac{112}{15}$ hours = $7$ hours $28$ minutes

Due to leakage, time taken = $7$ hrs $28$ min + $32$ min = $8$ hrs

Work done by (two pipes + leak) in $1$ hour $=\frac{1}{8}$

Work done by the leak in $1$ hour $=\frac{15}{112}-\frac{1}{8}$ $=\frac{1}{112}$

Leak will empty the full cistern in 112 hours.

• Pipes and Cisterns - Solved Examples
• Pipes and Cisterns - Data Sufficiency 1
• Pipes and Cisterns - Data Sufficiency 2