Sure, let's solve this problem step by step.
1. Initial Information 15 Years Ago:
- The average age of the husband and wife 15 years ago was 20 years.
- Therefore, the sum of their ages 15 years ago was [tex]\( 2 \times 20 = 40 \)[/tex] years.
2. Total Age Increase Over 15 Years:
- Each year both the husband and the wife age by 1 year. So, in 15 years, both of them will have aged by [tex]\( 15 \times 2 = 30 \)[/tex] years.
- Therefore, the total of their ages now is [tex]\( 40 + 30 = 70 \)[/tex] years.
3. Current Average Age with Children:
- Currently, the couple plus their two children have the same average age of 20 years.
- There are 4 people in total. Hence, the sum of their current ages is [tex]\( 4 \times 20 = 80 \)[/tex] years.
4. Total Age of the Children:
- We already calculated that the combined age of the husband and wife today is 70 years.
- Therefore, the combined age of their two children is [tex]\( 80 - 70 = 10 \)[/tex] years.
5. Ages of the Children:
- Let the age of the youngest child be [tex]\( x \)[/tex] years.
- Since the children differ in age by 2 years, the age of the oldest child will be [tex]\( x + 2 \)[/tex] years.
- The sum of their ages is given by [tex]\( x + (x + 2) = 10 \)[/tex].
6. Solve for [tex]\( x \)[/tex]:
- Simplify the equation: [tex]\( 2x + 2 = 10 \)[/tex].
- Subtract 2 from both sides: [tex]\( 2x = 8 \)[/tex].
- Divide both sides by 2: [tex]\( x = 4 \)[/tex].
Therefore, the present age of the youngest child is [tex]\( 4 \)[/tex] years.
So the correct answer is:
(c) 4 years
