Question

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

Accepted Answer

D. Let volume of jug be $v$. After two replacements, remaining orange juice = $10\left(1 - \frac{v}{10}\right)^2 = 5$. $\left(1 - \frac{v}{10}\right)^2 = 0.5 \implies 1 - \frac{v}{10} = \frac{1}{\sqrt{2}} \approx 0.707$. $\frac{v}{10} = 0.293 \implies v = 2.93$ litres. Since $2.93$ lies between $2.5$ and $3$, option D is correct.

Gopal Fruit Juice Replacement

Explanation

Practise this under exam conditions