Question
A mixture (alcohol + water) contains alcohol and water
in the ratio of 4:3, respectively. If 49 litres of the mixture is replaced with 21 litres of water, then quantity of alcohol in the final mixture becomes 28 litres more than that of water. Find the initial quantity of the mixture.Solution
Let the quantity of alcohol and water in the initial mixture be ‘4x’ litres and ‘3x’ litres, respectively Quantity of alcohol in 49 litres of the mixture
= 49 × (4/7) = 28 litres Quantity of water in 49 litres of the mixture
= 49 − 28 = 21 litres According to the question, (4x − 28) = (3x − 21 + 21) + 28 Or, 4x − 3x = 28 + 28 Or, x = 56 Initial quantity of the mixture = 7x = 7 × 56 = 392 litres
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