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Alligation or Mixture

Q1: 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

ANS:C -

1
5

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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