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?

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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: Option C

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