Question

In a mixture of 126 kg of milk and water, milk and water are in ratio 5:2. How much water must be added to the mixture to make this ratio 3:2?

Answer 1

Hint: A ratio is a comparison of values of two quantities of the same type and having the same unit by division. The ratio of two quantities a and b is the fraction $\dfrac{a}{b}$ and is written as a:b . The Milk and water are in ratio 5:2. The weight of milk in the mixture is 5x and water is 2x. Since the total weight of milk and water is 126kg. Therefore, 5x+2x=126.

Complete step-by-step answer:
The weight of the mixture of milk and water is 126 kg.
Milk and water are in ratio 5:2
Let the weight of milk in the mixture is 5x and water is 2x
Now, since the total weight of milk and water is 126kg.
So we have
5x+2x=126
7x=126
Therefore x= $\dfrac{{126}}{7}$
Now we have calculate value of x = 18
We will substitute value of x=18 to find out the weight of milk and water
So, the weight of milk in the mixture is 5x = 5 × 18 = 90 kg
 The weight of water in the mixture is 2x = 2 ×18 = 36 kg
Let y kg of water is added to the mixture to make the ratio of milk and water 3:2
Therefore, the weight of milk is 90 and water is 36+y.
Then we have
$ \Rightarrow \dfrac{{90}}{{36 + y}} = \dfrac{3}{2}$
$180 = 3\left( {36 + y} \right)$
36 + y = 60
y= 60-36
y= 24

The water that must be added to the mixture to make this ratio 3:2 is 24kg

Note: Additional Information,
Points to remember about ratios ,
The ratio is a fraction.
The ratio does not have a unit.
Units of both the quantities involved in a ratio have to be the same.
If you want to know whether your answer is correct or not so just add the values which you have got after substituting the value of variables.