Question

A milk can contains $112$ liter of milk. How many liters of milk should be removed and the same amount of water is added, the proportion of milk to water comes to be $13:3?$
A. $\dfrac{{336}}{{16}}$
B. $\dfrac{{158}}{{13}}$
C. $\dfrac{{178}}{{16}}$
D. $\dfrac{{138}}{{13}}$

Answer 1

Hint: First assume that the amount of milk that is removed from the can of milk and then find the ratio of the milk to the water and compare it with the given ratio to get the desired result.

Complete step by step solution:
It is given that a milk can contains $112$ liter of milk and we have to find how much milk should be removed and the same amount of water is added so that the ratio of the milk to the water becomes $13:3$.

First, assume that $x$ liters of milk should be removed from the container, then the remaining amount of milk becomes $\left( {112 - x} \right)$.
As given that the same amount of water is added to the milk, then the quantity of milk becomes $x$.

Now, we have analyzed the problem after the removal of some quantity of milk.
The amount of milk$ = 112 - x$
The amount of water$ = x$
Then the proportion of milk to water is given as:
Proportion$ = \dfrac{{{\text{Quantity of milk}}}}{{{\text{Quantity of water}}}}$
Proportion$ = \dfrac{{112 - x}}{x}$

We have given the proportion of the milk to the water is $13:3$, we can write
$\dfrac{{13}}{3} = \dfrac{{112 - x}}{x}$
Now, solve the equation for the value of $x$.
$13x = 3\left( {112 - x} \right)$
$ \Rightarrow 13x = 336 - 3x$
$ \Rightarrow 13x + 3x = 336$
$ \Rightarrow 16x = 336$
$ \Rightarrow x = \dfrac{{336}}{{16}}$
$ \Rightarrow x = 21$

So, the quantity of milk removed from the can is $21$ liter.

Note: The proportion of the milk to the water defines how much quantity of water in comparison to the milk in the can.