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      Question

      Initially, 40% of mixture ‘P’, consisting of petrol

      and diesel, is transferred into mixture ‘Q’, which has a petrol to diesel ratio of 5:4. After this transfer, the ratio of petrol to diesel in mixture ‘Q’ changes to 17:13. Following the transfer, the remaining quantities of petrol and diesel in mixture ‘P’ are 54 liters and 36 liters, respectively. Calculate the initial quantity of mixture ‘Q’.
      A 145 Correct Answer Incorrect Answer
      B 150 Correct Answer Incorrect Answer
      C 180 Correct Answer Incorrect Answer
      D 145 Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      ATQ, Ratio of petrol and diesel in the mixture ‘P’ = 54:36 = 3:2 60% of mixture ‘P’ = 54 + 36 = 90 litres Therefore, 40% of the mixture = (90/60) × 40 = 60 litres Quantity of petrol in 40% of mixture ‘P’ = 60 × 3/5 = 36 litres Quantity of diesel in 40% of mixture ‘P’ = 60 – 36 = 24 litres Let the quantity of petrol and diesel in the mixture ‘Q’ be 5q litres and 4q litres respectively. According to the question, (5q + 36)/(4q + 24) = 17/13 Or, 65q + 468 = 68q + 408 Or, 3q = 60 Or, q = 20 litres Total quantity of mixture ‘Q’ = 5q + 4q = 9q = 180 litres

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