Question
A mixture (paint + thinner) contains paint and thinner
in the ratio of 9:5, respectively. If 56 litres of the mixture is replaced with 28 litres of thinner, then quantity of paint in the final mixture becomes 32 litres more than that of thinner. Find the initial quantity of the mixture.Solution
Let the quantity of paint and thinner in the initial mixture be ‘9x’ litres and ‘5x’ litres, respectively Quantity of paint in 56 litres of the mixture
= 56 × (9/14) = 36 litres Quantity of thinner in 56 litres of the mixture
= 56 − 36 = 20 litres According to the question, (9x − 36) = (5x − 20 + 28) + 32 Or, 9x − 5x = 36 + 20 + 32 Or, 4x = 76 Or, x = 19 Initial quantity of the mixture
= 14x = 14 × 19 = 266 litres
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