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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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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?

posted Dec 8, 2015 by Brijesh Talwar

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2 Answers

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3+5=8
(3-1)+(5-1)=8-2
2+4=6
(2+2)+(4+0)=6+2
4+4=8

answer Dec 8, 2015 by Jaikumar Bhatia
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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/8 + x) litres

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

So  ( 3 -   3x/8    + x )    = ( 5 - 5x/8 )

So 5x + 24 = 40 - 5x

10x = 16

x = 8/5 .

So, part of the mixture replaced = ( 8/5 x 1/8 ) = 1/5

answer Dec 9, 2015 by Avantika Agrawal



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