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
Explanation:
Assume that the volume of the jug is l liters.
Hence, after first replacement, the juice mixture contains l liters of pineapple juice.
When the juice mixture is drawn out for the second time using the jug, the amount of pineapple juice in the jug = l × ( l / 10)
This is replaced by l litres of pineapple juice.
Hence, amount of pineapple juice after two replacements = l + ( l – l × ( l / 10)) = 5
Hence, we get,
l2 – 20l + 50 = 0
Solving the above quadratic we get,
l = 5(2 - √2) or l = 5(2 + √2)
As, 5(2 + √2) > 10, l = 5(2 - √2) ≈ 2.92
Hence, option (d).
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