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A serum bottle is filled with 4 parts of water and 5 parts of serum. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half serum?

A serum bottle is filled with 4 parts of water and 5 parts of serum. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half serum? Correct Answer 10%

Given:

A serum bottle is filled with 4 parts of water and 5 parts of serum.

Formula:

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

Final volume = initial volume × (1 – x/v)n

Calculation:

Final volume = initial volume × (1 – x/v)n

⇒ 1/2 = 5/9 × (1 – x/v)1

⇒ 9/10 = 1 – x/v

⇒ x/v = 1 – (9/10)

⇒ x = v/10

∴ 10% of the mixture will be drawn off.

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