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 leak in the bottom of a tank can empty the full tank in $8$ hours. An inlet pipe fills water at the rate of $6$ liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in $12$ hours. How many liters does the cistern hold ?

Answer:

Explanation:

Work done by the inlet in $1$ hour $=\left(\frac{1}{8}-\frac{1}{12}\right)$ $=\frac{1}{24}$.

Work done by the inlet in $1$ min. $=\left(\frac{1}{24}\times\frac{1}{60}\right)$ $=\frac{1}{1440}$.

$\therefore$ Volume of $\frac{1}{1440}$ part $= 6$ liters.

$\therefore$ Volume of whole $=(1440\times 6)$ liters = 8640 liters. 

A large tanker can be filled by two pipes $X$ and $Y$ in $60$ minutes and $40$ minutes respectively. How many minutes will it take to fill the tanker from empty state if $Y$ is used for half the time and $X$ and $Y$ fill it together for the other half?

Answer:

Explanation:

Part filled by $(X+Y)$ in $1$ minute $=\left(\frac{1}{60}+\frac{1}{40}\right)$ $=\frac{1}{24}$.

Suppose the tank is filled in $x$ minutes.

Then, $\frac{x}{2}\left(\frac{1}{24}+\frac{1}{40}\right)$  = 1.

$\Rightarrow\frac{x}{2}\times\frac{1}{15}$ $=1$

$\Rightarrow x=30$ min.

Two pipes $A$ and $B$ can fill a tank in $6$ hours and $14$ hours respectively. If they are opened on alternative hours and if pipe $A$ is opened first, in how many hours, the tank shall be full ?

Answer:

Explanation:

$A$’s work in $1$ hour $=\frac{1}{6}$

$B$’s work in $1$ hour $=\frac{1}{4}$

$(A+B)$’s $2$ hour’s work when opened alternatively $=\left(\frac{1}{6}+\frac{1}{4}\right)$ $=\frac{5}{12}$.

$(A+B)$’s $4$ hour’s work when opened alternatively $=\frac{10}{12}$ $=\frac{5}{6}$.

Remaining part $=\left(1-\frac{5}{8}\right)$ $=\frac{1}{6}$.

Now, it is $A$’s turn and $\frac{1}{6}$ part is filled by $A$ in $1$ hour.

$\therefore$ Total time taken to fill the tank $=(4+1)$ hrs = 5 hrs.

Three pipes X, Y and Z can fill a tank in $6$ hours. After working at it together for $2$ hours, $Z$ is closed and $X$ and $Y$ can fill the remaining part in $7$ hours. The number of hours taken by $Z$ alone to fill the tank is:

Answer:

Explanation:

Part filled in $2$ hours  $=\frac{2}{6}$  $=\frac{1}{3}$

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

$\therefore$  $(X+Y)$’s $7$  hour’s work $=\frac{2}{3}$.

$(X+Y)$’s $1$ hour’s work $=\frac{2}{21}$.

$\therefore$ $Z$’s $1$ hour’s work = $\{(X+Y+Z)$’s $1$ hour’s work$\}$  - $\{(X+Y)$’s $1$ hour’s work$\}$

$=\left(\frac{1}{6}-\frac{2}{21}\right)$ $=\frac{1}{14}$

$\therefore$ $Z$ alone can fill the tank in 14 hours

$12$ buckets of water fill a tank when the capacity of each tank is $13.5$ liters. How many buckets will be needed to fill the same tank, if the capacity of each bucket is $9$ liters ?

Answer:

Explanation:

Capacity of the tank  $=(12\times 13.5)$ liters = 162 liters.

Capacity of each bucket = 9 liters.

Number of buckets needed  $=\left(\frac{162}{9}\right)$ = 18

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