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A vessel is filled with a 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 is half water and half syrup?

A vessel is filled with a 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 is half water and half syrup? Correct Answer 1/5

Let, the initial quantity of liquid be 8x

⇒ Quantity of water initially = 8x × 3/8 = 3x

⇒ Quantity of Syrup initially = (8x – 3x) = 5x

Suppose, y lit of mixture is taken out and replaced with water

⇒ Quantity of water now = (3x – 3y/8 + y) = 3x + 5y/8

⇒ Quantity of syrup now = (5x – 5y/8)

According to the question,

3x + 5y/8 = 5x – 5y/8

⇒ 10y/8 = 2x

⇒ 10y = 16x

⇒ y = 8x/5

∴ Part of mixture drawn off = y/8x = 1/5 

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