How many litres of water should be added to a 65 litre mixture of milk and water containing milk and water in the ratio of 8 : 5 such that the resultant mixture contains 50% water?

Question: How many litres of water should be added to a 65 litre mixture of milk and water containing milk and water in the ratio of 8 : 5 such that the resultant mixture contains 50% water?

Solution:
Given that,
The mixture contains 65 litres of milk and water in the ratio 8 : 5.
Total parts = 8 + 5 = 13
Milk = (8/13) × 65 = 40 litres
Water = (5/13) × 65 = 25 litres

Let x litres of water be added.
∴ New water quantity = 25 + x litres
∴ New total mixture = 65 + x litres

The resultant mixture should contain 50% water.
(25 + x)/(65 + x) = 1/2
⇒ 2(25 + x) = 65 + x
⇒ 50 + 2x = 65 + x
⇒ 2x - x = 65 - 50
∴ x = 15

So 15 litres of water should be added.