Question
A fuel blend composed of diesel and petrol is mixed in a
ratio of 5:3, respectively. If one-fourth of this blend is removed and replaced with 24 liters of petrol, the resulting quantities of diesel and petrol are equal. Determine the initial volume of the mixture.Solution
Let the initial quantity of diesel and petrol in the mixture be 5x litres and 3x litres, respectively Final quantity of diesel in the mixture = 0.75 × 5x = 3.75x litres Final quantity of petrol in the mixture = (0.75 × 3x) + 24 = (2.25x + 24) According to the question, 2.25x + 24 = 3.75x Or, 1.5x = 24 Or, x = 16 Therefore, initial quantity of the mixture = 5x + 3x = 8x = 128 litres Hence, option c.
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