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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 drawn off and replaced with water so that the mixture may be half water and half syrup?

Correct Answer: 1 5

Explanation:

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 - 3x + x litres
8



Quantity of syrup in new mixture = 5 - 5x litres
8



3 - 3x + x = 5 - 5x
8 8


⟹ 5x + 24 = 40 - 5x


⟹ 10x = 16



x = 8 .
5



So, part of the mixture replaced = 8 x 1 = 1 .
5 8 5


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