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A glass 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 glass 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? Correct Answer 1/5

Given:

The ratio of water and syrup = 3 ∶ 5 

After replacement the ratio of water and syrup = 1 ∶ 1 

Concept used:

Always divide the mixture according to the initial ratio

Calculations:

Let the glass initially contain 8 litres of liquid.

Let y litres of this liquid must be replaced with water.

The quantity of water drawn off = 3y/8 

Remaining water = 3 – 3y/8 

Total water after replacement = 3 – 3y/8 + y

The quantity of syrup drawn off = 5y/8 

Remaining syrup = 5 – 5y/8

According to the questions

3 – 3y/8 + y = 5 – 5y/8

⇒ 3 + 5y/8 = 5 – 5y/8 

⇒ 10y/8 = 2 

⇒ y = 8/5

Part of mixture replaced = (1/8 of 8/5) = (1/5)th part 

∴ (1/5)th part of mixture must be drawn off 

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