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A vessel is filled with a liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

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\frac{1}{5}

\frac{3}{7}

\frac{4}{5}

\frac{3}{10}

answer is A.

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Detailed Solution

A vessel have filled with liquid part of water = 3
A vessel have filled with liquid part of syrup = 5
Total part of liquid = 3+ 5 = 8
Now, we have
Water = 3/8
Syrup = 5/8
Assume that
The amount of liquid which is replaced by water = x
Water

= \frac{3 x}{8}

Syrup=

\frac{5 x}{8}

Thus,
Water before replacement +

\frac{5 x}{8}

= syrup before replacement -

\frac{5 x}{8}

Syrup – water (before replacement)

= \frac{10 x}{8} = \frac{5 x}{4}

\Rightarrow 5 / 8 part - 3 / 8 part = 5 x / 4

\Rightarrow \frac{1}{4 part} = \frac{5 x}{4}

\Rightarrow x = 1 / 5

SO, 1/5 part of mixture should be drawn off and replaced with water.
Correct option is 1.

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