Question

In 80 litres pure milk, 8 litres of milk is replaced by water if this process is repeated two times then what will be the ratio of milk and water in the final mixture?
1. 81 ∶ 19
2. 19 ∶ 81
3. 63 ∶ 17
4. 17 ∶ 63

Answer 1

Correct Answer - Option 1 : 81 ∶ 19

Given:

Quantity of pure milk = 80 litres 

Quantity of milk removed and replaced by water = 8 litres

Formula used:

Amount of milk left = Initial amount × [1 – (Amount took out and replaced)/Initial amount]ⁿ 

Here n is the number of times the process repeated

Calculation:

Amount of milk left = 80 × [1 – 8/80]² 

⇒ 80 × (1 - 1/10)²

⇒ 80 × (9/10)²

⇒ 80 × (81/100) = 64.8 litres

Amount of water in the final mixture = 80 – 64.8 = 15.2 litres

The ratio of milk and water in the final mixture = 64.8 ∶ 15.2 = 81 ∶ 19

∴ The ratio of milk and water in the final mixture is 81 ∶ 19