Question

In a mixture of 100L, the ratio of milk and water is 3:1. If 200L of water is added to the mixture, what is the new ratio of milk and water?

Answer 1

Hint: First we will calculate the separate amount of water and milk present in a mixture of 100L then calculate the rate of water and milk after adding and then we can find the ratio of amount of milk and amount of water.

Complete step by step answer:
Given: we have given the amount of mixture which is equal to 100L and the ratio of milk and water is also given which is $3:1$ and we have to find the new ratio of milk and water after adding 200L of water in the given mixture.
As the mixture of 100L is given and the ratio of milk and water is $3:1$.
Now, let $x$ be the variable of constant value
Therefore, we will multiply the $x$ by 3 and 1 and then we will add both the value to find the separate value of milk and water and the obtained value will always be equal to the 100L of mixture.
Hence, $3x + 1x = 100{\text{L}}$
$
  4x = 100{\text{L}} \\
  x = 25{\text{L}} \\
 $
It means milk in a given solution is$3 \times 25{\text{L}} = 75{\text{L}}$ and water is $1 \times 25 = 25{\text{L}}$.
A new solution is to be formed in which we will add 200L of water.
New solution = 75L milk $ + $ 225L water
Hence the new ratio of milk is to water is $\dfrac{{{\text{amount of milk}}}}{{{\text{amount of water}}}}$
Mathematically, $\dfrac{{75}}{{225}} = 1:3$
So, $1:3$ is the ratio of new mixture after adding 200L of water. Where, 1 unit represents the milk and 3 units represent water in the mixture.

Note: We have taken the variable $x$ to break the ratio so is to find the milk and water in a proper amount then we have found the required ratio.