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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 will be half water and half syrup?

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 will be half water and half syrup? Correct Answer <span class="math-tex">\(\frac{1}{5}\)</span>

Let the Initial quantity of liquid be 8 litres

∴ After replacing ‘x’ litres with water,

Water in mixture = 3 - 3x/8 + x = 3 + 5x/8

Syrup in mixture = 5 - 5x/8

According to the given condition,

⇒ 3 + 5x/8 = 5 - 5x/8

∴ 5x/4 = 2

∴ x = 8/5

∴ For 8 litres, 8/5 of the mixtures must be taken off

∴ For 1 litre, 8/5 × 1/8 = 1/5 part must be replaced

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