The sum of the ages of 5 children born at intervals of 2 years each is 40 years. What is the age of the eldest

Question

The sum of the ages of 5 children born at intervals of 2 years each is 40 years. What is the age of the eldest child?

Examoogle · Accepted Answer

The correct answer is Option D: 16 years. For an odd number of terms in an AP, the sum divided by the number of terms gives the exact middle (median) term. Middle age = 40 / 5 = 8 years. Since the intervals are 2 years, the 5 children's ages are 4, 6, 8, 10, and 12 years. The eldest child is 12 years old.

Step-by-Step Solution & Concepts:
Shortcut Trick: For an odd number of terms in an AP, the sum divided by the number of terms gives the exact middle (median) term. Middle age = 40 / 5 = 8 years. Since the intervals are 2 years, the 5 children's ages are 4, 6, 8, 10, and 12 years. The eldest child is 12 years old.

Formula Used: $$S_n = \frac{n}{2} \cdot [2a + (n-1)d]$$

Given: Number of children = 5, Born at intervals of 2 years each (Arithmetic Progression with common difference d = 2), Sum of their ages = 40 years

Steps: Step 1: Set up the ages in Arithmetic Progression: Let the age of the youngest child be $x$. Since the 5 children are born at intervals of 2 years, their respective ages can be represented as: $x, x+2, x+4, x+6, 	ext{ and } x+8$.. Step 2: Formulate the sum equation: The problem states that the sum of the ages of these 5 children is 40 years. Adding all the expressions together: $x + (x+2) + (x+4) + (x+6) + (x+8) = 40$.. Step 3: Solve for the youngest child's age ($x$): Subtract 20 from both sides: $5x = 40 - 20 \implies 5x = 20$. Dividing by

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