1. The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 respectively. In what ratio the liquid of both the vessels should be mixed such that a new mixture containing half spirit and half water is obtained?
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By: anil on 05 May 2019 02.03 am
Spirit in 1 litre mixture of vessel 1 = $$frac{5}{6}$$ Spirit in 1 litre mixture of vessel 2 = $$frac{3}{10}$$ Spirit in 1 litre of the new mixture = $$frac{1}{2}$$ Let ratio of liquid from both vessels be $$x:y$$ => $$(frac{5}{6}x)+(frac{3}{10}y)=frac{1}{2}(x+y)$$ Multiply both sides by L.C.M. (6,10,2) = 30 => $$25x+9y=15x+15y$$ => $$25x-15x=15y-9y$$ => $$10x=6y$$ => $$frac{x}{y}=frac{6}{10}=frac{3}{5}$$ $$ herefore$$ Liquid of both the vessels should be mixed in the ratio 3 : 5 such that a new mixture containing half spirit and half water is obtained. => Ans - (A)
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