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’.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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