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

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Solution

Suppose the vessel initially contains 8 litres of liquid Let x litres of this liquid be replaced with water
Quantity of water in new mixture = $(3 - \frac{3 x}{8} + x)$ litres
Quantity of syrup in new mixture $(3 - \frac{5 x}{8})$ litres
$∴ (3 - \frac{3 x}{8} + x) = (5 - \frac{5 x}{8}) \Rightarrow 5 x + 24 = 40 - 5 x$
$\Rightarrow 10 x = 16 \Rightarrow x = \frac{8}{5}$
So part of the mixture replaced = $(\frac{8}{5} \times \frac{1}{8}) = \frac{1}{5}$

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

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