The sum of the present ages of five children, born at intervals of 3 years each, is 50 years. What is the present age of the youngest child?

Introduction / Context:
This problem involves several children whose ages form an arithmetic sequence, because each child is born 3 years after the previous one. The sum of their present ages is given, and we are asked to determine the age of the youngest child. This is a standard question under the topic problems on ages and arithmetic progressions.

Given Data / Assumptions:
There are five children. Each successive child is 3 years older than the next younger one, so their ages differ by 3 years. The sum of the present ages of all five children is 50 years. We are required to find the present age of the youngest child. Ages are treated as whole numbers in years.

Concept / Approach:
If the youngest child is x years old, then the other children are x + 3, x + 6, x + 9, and x + 12 years old, since they are each 3 years apart. The sum of these five ages can be expressed in terms of x. We then set this sum equal to 50, solve for x, and identify the youngest child's age.

Step-by-Step Solution:
Step 1: Let the present age of the youngest child be x years.Step 2: Because the children are born at intervals of 3 years, their ages are x, x + 3, x + 6, x + 9, and x + 12 years.Step 3: The sum of their ages is given as 50 years. So x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50.Step 4: Combine like terms: x + x + x + x + x = 5x, and 3 + 6 + 9 + 12 = 30. So the equation becomes 5x + 30 = 50.Step 5: Subtract 30 from both sides: 5x = 20.Step 6: Divide both sides by 5: x = 20 / 5 = 4 years.Step 7: Hence, the youngest child is 4 years old at present.

Verification / Alternative check:
Compute all ages: youngest 4 years, then 7, 10, 13, and 16 years. Their sum is 4 + 7 + 10 + 13 + 16 = 50 years, which matches the total given in the question. This confirms that the solution is correct and consistent with all the information provided.

Why Other Options Are Wrong:
If the youngest child were 6 years old, the ages would be 6, 9, 12, 15, and 18 years, summing to 60 years, not 50. If the youngest were 8 or 16 years old, the sums would be even larger and would clearly not equal 50 years. Therefore, those options do not satisfy the total sum condition.

Common Pitfalls:
Some learners may forget that there are five children and mistakenly use fewer terms in the arithmetic sequence. Others may miscalculate the sum of the constant differences (3, 6, 9, 12). Writing the sequence explicitly and adding carefully helps avoid such mistakes.

Final Answer:
The youngest child is 4 years old at present.