Question

# In a mixture of 60 litres, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is what?

Hint: This question has come from ratio and proportion. Here we will first obtain the quantity of both milk and water from given data. Then taking the quantity of water to be added as x we will equate the answer. We can also use alternative methods to solve this.

In the question it is given that,
Quantity of the mixture is 60 liters
The ratio of milk and water in that mixture is 2:1
Hence, the quantity of milk in the mixture is $\left( {60 \times \dfrac{2}{3}} \right) = 40 litres$
And the quantity of water in the mixture is $60 - 40 = 20 litres$
The needed new ratio of milk and water is 1:2
In the question it is asked to add water in the mixture that means the quantity of milk will remain the same.
Let the quantity of water to be added further is x litres
Then the ratio of milk and water will be $\dfrac{{40}}{{20 + x}}$
According to question, the ratio is $\dfrac{{1}}{{2}}$
Hence, $\dfrac{{40}}{{20 + x}} = \dfrac{1}{2}$
By cross multiplication we get,
$80 = 20 + x$
$\Rightarrow x = 80 - 20 = 60 litres$
Hence the quantity of water to be added is 60 litres.

Note: Error check: $\dfrac{{40}}{{20 + x}} = \dfrac{{40}}{{20 + 60}} = \dfrac{{40}}{{80}} = \dfrac{1}{2}$ (Error checked)
Alternative method- In the question it is given that,
Quantity of the mixture is 60 litres
The ratio of milk and water in that mixture is 2:1
Hence, the quantity of milk in the mixture is $\left( {60 \times \dfrac{2}{3}} \right) = 40 litres$
And the quantity of water in the mixture is $60 - 40 = 20 litres$
The needed new ratio of milk and water is 1:2
Let in the new mixture, quantity of milk be x and quantity of water be 2x
In the question it is asked to add water in the mixture that means the quantity of milk will remain the same.
Hence, $x = 40$ litres
Then, quantity of water, $2x = 80$ litres
Quantity of water needed to be added is $80 - 20 = 60 litres$.