The problem is that the question is cleverly phrased to conceal what is really going on.

Let’s locate all that money. There are two ways to think about how much money is out there to be found.The way that this question is tricky is that it combines that two ways.

The first way is this. How much money did the three men pay originally?

The second way is this. How much money did they end up paying?

So if it is the first way, then clearly the total we need to account for is the $15.

So let’s see what happens to that $15. The chef gets $10, the waiter gets $2 and the guys get $3 back. That adds up fine.

Now let’s look at the second way. How much money did they end up paying? Well $12 dollars, and $10 of it went to the chef and $2 to the waiter. Now, that adds up too.

The problem with the question is that the the $2 that the waiter took is contained in the $12 that they end up paying so we shouldn’t expect them to add to anything meaningful.