Question

A water tank is $\dfrac{2}{5}th$ full. The pipe $A$ can fill the tank in $10{\text{ minutes}}$ and the pipe $B$ can empty it in ${\text{6 minutes}}$. If both the pipes are open, how long will it take to empty or fill the tank?
$\left( a \right){\text{ 6 minutes to empty}}$
$\left( b \right){\text{ 6 minutes to fill}}$
$\left( c \right){\text{ 9 minutes to empty}}$
$\left( d \right){\text{ 9 minutes to fill}}$

Answer 1

Hint:
This type of problem can be solved in more than one way. So for this in $1{\text{ minute}}$ pipe $A$ fills $\dfrac{1}{{10}}th$ part and similarly, $1{\text{ minute}}$ pipe $B$ fills $\dfrac{1}{6}th$ part. Now by subtracting both the work we will get the total work done. Then by using the unitary method we can easily get to the solution.

Complete step by step solution:
First of all, we will see the time taken to fill a certain part by both the pipes.
So in $1{\text{ minute}}$ pipe $A$ fills $\dfrac{1}{{10}}th$ part and similarly,
In $1{\text{ minute}}$ pipe $B$ fills $\dfrac{1}{6}th$ part.
Therefore, the total work done by both the pipe that is $\left( {A + B} \right)$ in $1{\text{ minute}}$, we get
$ \Rightarrow \dfrac{1}{{10}} - \dfrac{1}{6}$
Now on solving the above, we get
$ \Rightarrow \dfrac{1}{{15}}$
So we can say that
$\dfrac{1}{{15}}th$, parts get emptied in $1{\text{ minute}}$
By using the unitary method, we get
So, $\dfrac{2}{5}th$ the part is emptied in
$ \Rightarrow 15 \times \dfrac{2}{5}\min $
And on solving the expression, we get
$ \Rightarrow 6{\text{ minute}}$.
So it takes $6{\text{ minute}}$ to empty the tank.

Therefore, the option $\left( a \right)$ is correct.

Additional information:
This type of problem is similar to time and work. And by supposing the pipes as a positive work and the leaks from the pipes as a negative work it gets easier to solve them. In this mainly two types of questions will be asked one is the rate at which the two pipes or tanks fill the tanks in such time respectively and the other one is a problem related to drainage or leakage.

Note:
This type of question can also be solved by supposing the tank of some liters and then will solve accordingly by using the unitary method. It will become easier and will also save time when we are doing competitive questions.