There are two glasses A and B. A contains orange juice and B contains apple…

2023

There are two glasses A and B. A contains orange juice and B contains apple juice in same quantity. Some amount orange juice from glass A is transferred to glass B. The juice is glass B is mixed well. Then again the same amount of juice from B is transferred to A. Ratio of quantities of apple juice in A and orange juice in B.

  1. A.

    1:1

  2. B.

    2:1

  3. C.

    1:2

  4. D.

    1:3

Attempted by 2 students.

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Correct answer: A

Let each glass initially contain V litres. Glass A contains only orange and glass B contains only apple. Transfer x litres from A to B.

  1. After the first transfer: A has orange = V - x (no apple). B has apple = V and orange = x, so total in B = V + x.

  2. Now mix B thoroughly and transfer x litres back from B to A. The fraction of apple in B is V/(V + x), so apple moved to A = x * V/(V + x). The fraction of orange in B is x/(V + x), so orange moved back to A = x * x/(V + x) = x^2/(V + x).

  3. Compute the two quantities of interest: apple in A after the second transfer = x * V/(V + x). Orange remaining in B = initial orange in B (x) minus orange transferred back (x^2/(V + x)) = x - x^2/(V + x) = x * V/(V + x).

Therefore the quantity of apple in the first glass equals the quantity of orange in the second glass; the ratio is 1:1.

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