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- A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup.
Question 1:
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
Feedback 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+ xlitres
Quantity of syrup in new mixture =5 -5x/8litres
3 -3x/8+ x=5 -5x/8
5x + 24 = 40 - 5x
10x = 16
x =8/5.
So, part of the mixture replaced = 8/5x1/8=1/5.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture =3 -3x/8+ xlitres
Quantity of syrup in new mixture =5 -5x/8litres
3 -3x/8+ x=5 -5x/8
5x + 24 = 40 - 5x
10x = 16
x =8/5.
So, part of the mixture replaced = 8/5x1/8=1/5.
D. 1/7
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