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A vessel is filled with liquid, 3 parts of which are water and 5 parts of 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)
    1/6
Correct answer is option 'C'. Can you explain this answer?
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A vessel is filled with liquid, 3 parts of which are water and 5 parts...
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A vessel is filled with liquid, 3 parts of which are water and 5 parts...
Given:
3 parts of water
5 parts of syrup

Let the total quantity of liquid be x.
Therefore, the quantity of water = (3/8)x
And the quantity of syrup = (5/8)x

Let y be the quantity of the mixture to be replaced with water.

After y quantity of mixture is replaced with water, the quantity of water in the mixture becomes:
(3/8)x - (3/8)y + y

And the quantity of syrup in the mixture becomes:
(5/8)x - (5/8)y

According to the problem, we need to find y such that the quantity of water becomes equal to the quantity of syrup in the mixture, i.e.,

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

Simplifying the equation, we get:

y = (1/5)x

Therefore, 1/5th of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup.

Hence, option (C) is the correct answer.
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A vessel is filled with liquid, 3 parts of which are water and 5 parts...
Correct answer 'C'
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