1. In a container, two types of liquids P and Q are in the ratio of 3 : 7. If 10 litres mixture is drawn off from the container and filled with 6 litres of liquid Q, then the ratio of P and Q becomes 1 : 3. What was the original quantity (in litres) of mixture?
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By: anil on 05 May 2019 02.05 am
Let original quantity of mixture = $$100x$$ litres => Quantity of P = $$30x$$ and Q = $$70x$$ litres If 10 litres mixture is drawn, => quantity of P taken out = 3 litres and Q = 7 litres
6 litres of liquid Q is added, thus new ratio => $$frac{30x-3}{70x-7+6}=frac{1}{3}$$ => $$frac{30x-3}{70x-1}=frac{1}{3}$$ => $$90x-9=70x-1$$ => $$90x-70x=9-1$$ => $$20x=8$$ => $$x=frac{8}{20}=0.4$$ $$ herefore$$ Original quantity of mixture = $$100 imes0.4=40$$ litres => Ans - (D)
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6 litres of liquid Q is added, thus new ratio => $$frac{30x-3}{70x-7+6}=frac{1}{3}$$ => $$frac{30x-3}{70x-1}=frac{1}{3}$$ => $$90x-9=70x-1$$ => $$90x-70x=9-1$$ => $$20x=8$$ => $$x=frac{8}{20}=0.4$$ $$ herefore$$ Original quantity of mixture = $$100 imes0.4=40$$ litres => Ans - (D)