Question

 

A vessel is filled with 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?

A. 1 3 B. 1 4 C. 1 5 D. 1 7

Answer 1

Answer is C

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 = $(3-\frac{3x}{8}+x)$ litres

Quantity of syrup in new mixture = $(5-\frac{5x}{8})$ litres

$(3-\frac{3x}{8}+x)$ = $(5-\frac{5x}{8})$

5x + 24 = 40 - 5x

10x = 16

∴ x = $(\frac{8}{5})$

So, the part of mixture replaced = $(\frac{8}{5} * \frac{1}{8})$ = $\frac{1}{5}$