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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?1). \(\frac{1}{3}\)2). \(\frac{1}{4}\)3). \(\frac{1}{5}\)4). \(\frac{1}{7}\) |
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Answer» 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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