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# Mixture and Alligation #13

 13. A vessel is filled with liquid, 3 parts of which are water and 5 parts are 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. $\dfrac{1}{3}$ B. $\dfrac{1}{4}$ C. $\dfrac{1}{5}$ D. $\dfrac{1}{6}$

Explanation:

Let the quantity of the liquid in the vessel = 8 litre. Then,
quantity of water in the liquid = 3 litre,
and quantity of syrup in the liquid = 5 litre.

Suppose $x$ litre of the mixture is drawn off and replaced with water. Then,
Quantity of water in the new mixture
$=3-\dfrac{3x}{8}+x$
Quantity of syrup in the new mixture
$=5-\dfrac{5x}{8}$

Given that in the new mixture, quantity of water = quantity of syrup
$\Rightarrow 3 - \dfrac{3x}{8} + x = 5 - \dfrac{5x}{8}\\\Rightarrow \dfrac{10x}{8} = 2 \\\Rightarrow \dfrac{5x}{4} = 2\\\Rightarrow x = \dfrac{8}{5}$

i.e., if the quantity of the liquid is 8 litre, $\dfrac{8}{5}$ litre of the mixture needs to be drawn off and replaced with water so that the mixture may be half water and half syrup.

It means $\dfrac{1}{5}$ of the mixture needs to be drawn off and replaced with water so that the mixture may be half water and half syrup.

pal
2016-09-22 10:25:12
suppose total mixture is 80 so

(30-3x/8)+x=50-5x/8
x=16

here 16 is 1/5 of 80 so we have to have this amount