A class has average age 35 years. Six new students with average age 33 years join, decreasing the overall average by 0.5 year. What was the original class strength?

Introduction / Context:When adding a subgroup changes the average by a small amount, set up an equation using totals before and after the addition. Unknown original strength can be solved from the equality of the new average.

Given Data / Assumptions:

• Original mean = 35; original size = N (unknown).
• New group: 6 students with mean = 33.
• New mean after joining = 35 − 0.5 = 34.5.

Concept / Approach:Equation: (35N + 6 * 33) / (N + 6) = 34.5. Solve for N with basic algebra.

Step-by-Step Solution:

Verification / Alternative check:Totals: original 35 * 18 = 630; new group total 6 * 33 = 198; combined = 828 over 24 people gives 828 / 24 = 34.5, confirming the drop by 0.5 year.

Why Other Options Are Wrong:14, 16, 20: Do not satisfy the new-average equation.

Common Pitfalls:Using unweighted averaging of 35 and 33 or misplacing the 0.5 decrease on only one student instead of across the whole class.

Final Answer:18