Five children are born at intervals of 3 years each. If the sum of their present ages is 50 years, what is the age of the youngest child?

Problem restatementThe ages form an arithmetic progression with common difference 3. Given the sum is 50, find the youngest child's age.

Given data

• 5 children, each 3 years apart.
• Sum of present ages = 50 years.

Concept/ApproachLet the youngest be x years. Then ages are x, x+3, x+6, x+9, x+12. Sum them and solve for x.

Step-by-step calculation x + (x+3) + (x+6) + (x+9) + (x+12) = 50 5x + 30 = 50 5x = 20 → x = 4

Verification/AlternativeAges would be 4, 7, 10, 13, 16. Sum = 4 + 7 + 10 + 13 + 16 = 50 (matches).

Common pitfalls

• Using the average (50/5 = 10) as the youngest; that is the middle term, not the youngest.

Final Answer4 years