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A moisturizer has 8 parts of vitamin C and 1 part of vitamin A. What percentage of this moisturizer can be drawn off and replaced with vitamin A so that the concentration of vitamin C is 75%?

A moisturizer has 8 parts of vitamin C and 1 part of vitamin A. What percentage of this moisturizer can be drawn off and replaced with vitamin A so that the concentration of vitamin C is 75%? Correct Answer 15.625

Given:

A moisturizer has 8 parts of vitamin C and 1 part of vitamin A. 

Formula:

When x is a part of mixture that has drawn off and v is the total volume.

Final = initial (1 – x/v)n

Calculation:

Final = initial (1 – x/v)n

75% = 75/100 = 3/4

⇒ 3/4 = 8/9 (1 – x/v)

⇒ x = (5/32) v

Converting 5/32 into percentage

(5/32) × 100 = 125/8 = 15.625%

Therefore 15.625% of the mixture will be drawn off.

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