Question

A container having pure milk, 30% is replaced by water and the process is repeated three times. At the end of the third operation, what will be the intensity of milk?

1. 34%
2. 35%
3. 38%
4.

34.3%

5. 36%

Answer 1

Correct Answer - Option 4 :

34.3%

Given:

Percentage of water replaced after three process = 30%

Formula used:

Quantity of milk left = a{1 – (b/a)}ⁿ

a = Initial quantity

b = Replaced quantity

n = Number of repetition

Calculation:

Let the initial quantity of milk be 100 l

⇒ Quantity of milk replaced with water = (30/100) × 100 = 30 l

n = 3

Quantity of milk left = 100{1 – (30/100)}³

⇒ Quantity of milk left = 100{(10 – 3)/10}³

⇒ Quantity of milk left = 100 × (7/10) × (7/10) × (7/10)

⇒ Quantity of milk left = 34.3%

∴ The intensity of milk after third operation is 34.3%