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Two Juices

Puzzle:

An orange colored glass has Orange juice and white colored glass has Apple juice both of equal volumes. 50ml of the orange juice is taken and poured into the white glass. After that similarly, 50ml from the white glass is poured into the orange glass. Of the two quantities, the amount of apple juice in the orange glass and the amount of orange juice in the white glass, which one is greater and by how much?

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Solution:

The two quantities are equal.

Solve it by taking example. Let's assume that both glasses contain 450 ml of juice each. Now, 50ml of the orange juice is taken and poured into the White glass. Hence, orange colored glass contains 400 ml of Orange juice and white glass contains 450 ml of Apple juice and 50 ml of Orange juice i.e. total of 500 ml from white glass contains 450 ml of Apple juice and 50 ml of Orange juice. It means that every 50 ml from white glass contains 45 ml of Apple juice and 5 ml of Orange juice. Similarly, 50 ml of juice from white glass is poured into orange glass. Now this 50 ml is not a pure apple juice. It contains 45 ml of Apple juice and 5 ml of Orange juice. Hence, Orange glass contains 405 ml of Orange juice and 45 ml of Apple juice. Similarly, white glass contains 405 ml of Apple juice and 45 ml of Orange juice.



21 comments:

ankit_blacki said...

surely, both the quantities would be same...
i concluded it mathematically
if anyone have any other logic?
kindly tell

Anonymous said...

yes, certainly they are the same.
if the volume of juices in each glass be x, then


apple juice in orange glass=50x/[50+x]
orange juice in white glass=50-250/[50+x]=50x/[50+x]

pg... said...

Both are same

Anonymous said...

You don't need to waste your time with examples and working out fractions, plus you assume that the juices are intermixed evenly which might not be the case.

You just need to know that after the two transfers, the same amount of liquid is in each glass as originally. Therefore whatever amount of orange juice is missing from the orange glass MUST be the same volume as the amount of apple juice that has replaced it.

Abhishek said...

You cannot conclude both are same from 1 example.
There can be 3 conditions:
1. White glass has more concentrate of apple juice then orange juice
2. orange glass has more concentrate of apple juice then orange juice
3. Both glasses have equal amount of apple and orange juice.

It depends on the total volume of juice present in each glass.
Eg:If 50ml > 1/2 volume of juice, then obviously the other glass will have more concentrate of the poured juice.

S.Guru said...

Both are same

S.Guru said...

Both are same

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