1. A vessel contains a mixture of milk and water in the respective ratio of 14 : 3. 25.5 litres of the mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of pure milk is added to the mixture. If the resultant mixture contains 20% water, what was the initial quantity of mixture in the vessel before the replacement? (in litres)
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- By: anil on 05 May 2019 01.37 amLet the total quantity of mixture in the vessel initially = $$17x$$ litres => Quantity of milk = $$frac{14}{17} imes 17x = 14x$$ litres Quantity of water = $$17x - 14x = 3x$$ litres Acc. to ques, => $$frac{14x - (frac{14}{17} imes 25.5) + 5}{3x - (frac{3}{17} imes 25.5) + 2.5} = frac{80}{20}$$ => $$frac{14x - 21 + 5}{3x - 4.5 + 2.5} = frac{4}{1}$$ => $$frac{14x - 16}{3x - 2} = frac{4}{1}$$ => $$14x - 16 = 12x - 8$$ => $$14x - 12x = 16 - 8$$ => $$x = frac{8}{2} = 4$$ $$ herefore$$ Initial quantity of mixture in the vessel before the replacement = $$17 imes 4 = 68$$ litres
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