Ravi has 1458 litres of a mixture of milk and water. The ratio of milk to water in this mixture is 8 : 1. How much water (in litres) should Ravi add into the mixture so that the ratio of milk and water becomes 6 : 5?

Correct option is A

Given:
Total mixture = 1458 litres

Initial ratio of milk to water = 8 : 1

Final ratio of milk to water = 6 : 5

Concept Used:

The quantity of milk remains constant when water is added. We can use this fact to set up a proportion and solve for the amount of water to be added.

Solution:
Initial quantity of milk:
Milk fraction =$$\frac{ 8 }{ (8 + 1) }= \frac{8}{9}$$​​
Quantity of milk = $$\frac{8}{9}\times 1458 = 1296 \text{litres}$$​

Let 'x' be the amount of water added.

New quantity of water = $$\frac{1}{9}\times1458 + x$$ = 162 + x

​$$\frac{\text{Milk}}{\text{Water} + x} = \frac{6}{5}$$​

​$$\frac{1296}{162 + x} = \frac{6}{5}$$​

6480 = 972 + 6x

6x = 6480 - 972

6x = 5508

x = $$\frac{5508 }{ 6}$$​

x = 918

Ravi should add 918 litres of water.

Option (A) is right.