Question
Initially, 40% of mixture βPβ, consisting of petrol
and diesel, is transferred into mixture βQβ, which has a petrol to diesel ratio of 5:4. After this transfer, the ratio of petrol to diesel in mixture βQβ changes to 17:13. Following the transfer, the remaining quantities of petrol and diesel in mixture βPβ are 54 liters and 36 liters, respectively. Calculate the initial quantity of mixture βQβ.Solution
ATQ, Ratio of petrol and diesel in the mixture βPβ = 54:36 = 3:2 60% of mixture βPβ = 54 + 36 = 90 litres Therefore, 40% of the mixture = (90/60) Γ 40 = 60 litres Quantity of petrol in 40% of mixture βPβ = 60 Γ 3/5 = 36 litres Quantity of diesel in 40% of mixture βPβ = 60 β 36 = 24 litres Let the quantity of petrol and diesel in the mixture βQβ 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 βQβ = 5q + 4q = 9q = 180 litres
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