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# 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?

Last updated date: 21st Jun 2024
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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.

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