Ina mixture of milk and water of 120 litres, the ratio of milk to water is 2 : 1. If the ratio of milk to water needs to be 1: 2, then the amount of water that needs to be added to the mixture is:

Correct option is B

Given:

mixture = 120 litres

initial ratio = 2:1

final ratio = 1:2

Solution:

Given that the ratio of milk to water is 2:1

, let the amount of milk be $2x$ and the amount of water be $x$.

The total volume of the mixture is 120 litres,

so:

2x+x=120

3x=120

x=40

milk = 80 litres

 water = 40 litres

 let the new amount of water added to make ratio 1:2 =y

​$$\frac{\text{Milk}}{\text{Water}} = \frac{1}{2} \\\frac{80}{40 + y} = \frac{1}{2} \\2 \times 80 = 40 + y \\160 = 40 + y \\y = 160 - 40 = 120$$​​

the new amount of water added =120litres

2x+x3x=1203x = 120