Easy math puzzles

Let's say that you start with 15 ml of milk and 250 ml of coffee. You move one teaspoon (5 ml) of milk into the coffee mug.

The ratio of coffee to total volume becomes 250/255 which is about 98%. Then, you take one teaspoon (5ml) of the 98% coffee + 2% milk mixture and dump it into the milk container. This teaspoon is 98% coffee and 2% milk, so .98*5ml coffee = 4.9 ml and 0.1 ml milk.

The milk container had 10 ml of milk after a teaspoon of it was removed. After adding back 5 ml, its volume is again 15 ml, and most of that, but not all, that is returned (98%) is coffee.

The amount of coffee in the milk cup is 4.901961 ml. The amount of milk in the coffee cup is 5 ml.

Quote: KevinAA

Let's say that you start with 15 ml of milk and 250 ml of coffee. You move one teaspoon (5 ml) of milk into the coffee mug.

The ratio of coffee to total volume becomes 250/255 which is about 98%. Then, you take one teaspoon (5ml) of the 98% coffee + 2% milk mixture and dump it into the milk container. This teaspoon is 98% coffee and 2% milk, so .98*5ml coffee = 4.9 ml and 0.1 ml milk.

The milk container had 10 ml of milk after a teaspoon of it was removed. After adding back 5 ml, its volume is again 15 ml, and most of that, but not all, that is returned (98%) is coffee.

The amount of coffee in the milk cup is 4.901961 ml. The amount of milk in the coffee cup is 5 ml.
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I'm not sure where your mistake is, but here are the amounts and ratios after each movement.

After first movement

Cup	Coffee	Milk	Total	Ratio Coffee	Ratio Milk
Coffee	250	5	255	0.980392	0.019608
Milk	0	10	10	0.000000	1.000000

After second movement

Cup	Coffee	Milk	Total	Ratio Coffee	Ratio Milk
Coffee	245.0980392	4.901960784	250	0.980392	0.019608
Milk	4.901960784	10.09803922	15	0.326797	0.673203

Note the milk in the coffee cup = coffee in the milk cup = 4.901960784.

We at least agree there is 4.901960784 ml of coffee in the milk cup. That had to displace the same amount of milk that used to be there. Where else could it have gone but the coffee cup?

OK, I get it now. That was a good one!