The sum of the present ages of four children born at intervals of 4 years each is 60 years. What is the present age of the youngest child?

Introduction / Context:
This problem deals with ages of children born at equal intervals of time. Since the children are born at intervals of 4 years, their ages form an arithmetic sequence. We are given the total of their present ages and asked to compute the age of the youngest child. This is a common type of question in aptitude exams for practicing arithmetic progressions and basic algebra.

Given Data / Assumptions:
- There are four children in the family.
- Each child is 4 years older than the next younger child.
- The sum of the present ages of all four children is 60 years.
- Ages are in complete years.
- We need to find the present age of the youngest child.

Concept / Approach:
When children are born at equal intervals of time, their ages form an arithmetic sequence. If we let the youngest child's age be x years, then the other children will be x + 4, x + 8, and x + 12 years old. The sum of these four expressions must equal the given total of 60 years. This leads to a simple linear equation in x that can be solved directly.

Step-by-Step Solution:
Step 1: Let the present age of the youngest child be x years.Step 2: Since the children are born at 4 year intervals, the other children are x + 4, x + 8, and x + 12 years old.Step 3: The sum of their present ages is x + (x + 4) + (x + 8) + (x + 12) = 60.Step 4: Combine like terms: x + x + x + x = 4x and 4 + 8 + 12 = 24, so the equation becomes 4x + 24 = 60.Step 5: Subtract 24 from both sides to obtain 4x = 36.Step 6: Divide both sides by 4 to get x = 36 / 4 = 9 years.Step 7: Therefore, the youngest child is 9 years old at present.

Verification / Alternative check:
Using x = 9, the ages of the four children are 9, 13, 17, and 21 years. The differences between consecutive ages are 4 years, as required. The sum 9 + 13 + 17 + 21 equals 60 years, matching the total given in the problem. This confirms that the youngest child's age has been calculated correctly.

Why Other Options Are Wrong:
If the youngest child were 7 years old, the ages would be 7, 11, 15, and 19 years, and their sum would be 52, not 60. If the youngest child were 10, 12, or 5 years old, the sums of the resulting age sequences would also not equal 60. Therefore, those values are inconsistent with the data and cannot be correct answers.

Common Pitfalls:
A frequent mistake is to misinterpret the phrase "born at intervals of 4 years" and incorrectly assign ages. Another error is to forget that there are exactly four children and write too many or too few terms. Some learners also add the constants incorrectly when forming the sum. Writing the ages in order and then summing them carefully helps avoid these issues.

Final Answer:
The youngest child is 9 years old at present.