A father has three sons. The youngest son is half the age of the middle son, and the oldest son is twice the age of the middle son. If the sum of their ages is 42 years, how old is each son?
The youngest son is 6 years old, the middle son is 12 years old, and the oldest son is 24 years old.

Here's the reasoning behind this:

1. Let's use variables to represent the ages of the sons: Y for the youngest son, M for the middle son, and O for the oldest son.
2. We know that Y = 0.5M and O = 2M from the information given in the question.
3. We also know that the sum of their ages is 42 years, so Y + M + O = 42.
4. Now we can substitute the expressions for Y and O from step 2 into the equation from step 3: 0.5M + M + 2M = 42.
5. Simplifying the equation gives us 3.5M = 42.
6. Dividing both sides by 3.5, we find that M = 12.
7. Now that we know the age of the middle son, we can easily find the ages of the other two sons using the expressions from step 2: Y = 0.5(12) = 6 and O = 2(12) = 24.
8. Therefore, the youngest son is 6 years old, the middle son is 12 years old, and the oldest son is 24 years old.