1. Gopal sells fruit juice mixture using orange juice and pineapple juice. Gopal prepares this mixture by drawing out a jug of orange juice from a 10 litre container filled with orange juice, and replacing it with pineapple juice. If Gopal draws out another jug of the resultant mixture and replaces it with pineapple juice, the container will have equal volumes of orange juice and pineapple juice. The volume of the jug in litres, is
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By: anil on 05 May 2019 02.37 am
Let volume of jug = $$v$$ litre After first replacement, volume of orange juice = $$(10 - v)$$ litre Volume of pineapple juice = $$v$$ litre After second replacement, volume of orange juice remaining = $$(10 - v) - (frac{10 - v}{10} v) = frac{(10 - v)^2}{10}$$ Volume of pineapple juice remaining = $$v - frac{v^2}{10} = frac{v (10 - v)}{10}$$ Total volume of pineapple juice = $$frac{v (10 - v)}{10} + v = frac{20v - v^2}{10}$$ It is given that container has equal volumes of both juices. => $$frac{(10 - v)^2}{10} = frac{20v - v^2}{10}$$ => $$v^2 - 20v + 50 = 0$$ => $$v = 17.07 , 2.93$$ $$ecause$$ Container is 10 litres, => $$v eq 17.07$$ $$ herefore v = 2.93$$ litres
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eq 17.07$$ $$ herefore v = 2.93$$ litres