# There are two cups filled with equal amount of tea and coffee. A spoonful of coffee is first transferred from coffee-cup to the tea-cup and then a spoonful from the tea-cup is transferred to the coffee-cup, then?

## The options are: 1. Amount of tea in the coffee-cup is more than the amount of coffee in the tea-cup. 2. Amount of coffee in the tea-cup is more than the amount of tea in the coffee-cup. 3. Amount of coffee in the tea-cup is the same as the amount of tea in the coffee-cup. 4. These amounts cannot be compared unless the volume of spoon and that of the cups are known.

Nov 12, 2016

3. The amounts are the same.

#### Explanation:

The assumptions I will make are:

• The spoonfuls transferred are of the same size.

• The tea and coffee in the cups are incompressible fluids which do not react with one another.

It does not matter if the drinks are mixed after the transfer of the spoonfuls of liquid.

Call the original volume of liquid in the coffee cup ${V}_{c}$ and that in the teacup ${V}_{t}$.

After the two transfers, the volumes are unchanged. If the final volume of tea in the coffee cup is $v$, then the coffee cup ends up with $\left({V}_{c} - v\right)$ coffee and $v$ tea. Where is the missing $v$ of coffee? We put it in the tea cup.

So the volume of coffee in the tea cup is also $v$.