Question 48

There are two cups, one containing orange juice and one containing an equal amount of lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in the orange juice or more orange juice in the lemonade?

Solution

Let the orange juice be in cup A initially and lemonade in B.

Let their vol. be 40L.

Let the vol. of the teaspoon be 10L.

On taking out 10L of orange juice from A and putting it in B, vol. of A becomes 30L and that of B becomes 50L.

In B, the ratio of vol. of orange juice to lemonade is 1:4.

Further when we take a teaspoon of the mixture from B, the vol. of liquid in the teaspoon will also have orange juice to lemonade in the ratio 1:4 i.e. 2L of orange juice and 8L of lemonade which is put into A.

So finally A contains 8L of lemonade and B contains 8L of orange juice because the teaspoon initially put in 10L and then took 2L out.


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