Answers

2015-10-06T14:55:13+05:30
They are   the same.

After both swaps have taken place, both cups contain the same amount of liquid that they each started with.

So, any tea missing from the cup of tea is now in the cup of coffee.

The same amount of coffee must be now missing from the cup of coffee, and must be in the cup of tea.

This can also be shown using algebra:

If each cup contains 100 units of its respective beverage and a spoon holds 10 units, then at the start we have:
Coffee Cup = 100 Coffee
Tea Cup    = 100 Tea
We now transfer a spoonful of tea across to the coffee to give:
Coffee Cup = 100 Coffee + 10 Tea
Tea Cup    = 90  Tea
We now transfer a spoonful of the coffee/tea mixture back to the tea cup, this 10 unit spoonful will contain [10 x (100 Coffee + 10 Tea) / 110].
So we will have: Coffee Cup = 100 Coffee + 10 Tea - [10 x (100 Coffee + 10 Tea) / 110]
Tea Cup    = 90  Tea + [10 x (100 Coffee + 10 Tea) / 110]
If we simplify this we get: Coffee Cup = (10000 / 110) Coffee + (1000 / 110) Tea
Tea Cup    = (10000 / 110) Tea    + (1000 / 110) Coffee
So there is as much coffee in the tea cup as there is tea in the coffee cup!
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