Question

From a container of milk, 10 % of the milk is replaced by water. This is repeated thrice. At the end of the third replacement, what percentage of pure milk is present in the mixture?
1. 73%
2. 70%
3. 80%
4. 30%

Answer 1

Correct Answer - Option 1 : 73%

Given 

Let pure milk = 100 

Water is replaced  in 10% in per process = 10% of 100 = 10 liter

Formula used 

Quantity of Milk present after replacing  = X × [1 - (Y/X)]ⁿ

here , X = initial  quantity of milk , Y = replaced water in per process , n = no of process repeated

Calculation 

Let pure milk = 100 

Water is replaced  in 10% in per process = 10% of 100 = 10 liter

Quantity of milk present = 100 × [1-10/100]³

⇒ 100 × [1-1/10]³

⇒ 100 × 729/1000

⇒ 72.9%

∴ The percentage of pure milk is present in the mixture is 73%.