The average age of 40 students in a class is 16 years. When a new student is admitted, the average increases by 0.2 years. What is the age of the new student?

Correct — A. Compare the class totals before and after.

Old total: 40 × 16 = 640
New average: 16 + 0.2 = 16.2
New total: 41 × 16.2 = 664.2

Subtract: new student = 664.2 − 640 = 24.2 years → option (a)
Shortcut: 16 + 41 × 0.2 = 16 + 8.2 = 24.2

Why the others are wrong

• (b)
  20.2 — With 20.2 the new total is 660.2, and 660.2 ⁄ 41 ≈ 16.10. The average would rise by about 0.1, not 0.2.
• (c)
  19.2 — With 19.2 the new total is 659.2, and 659.2 ⁄ 41 ≈ 16.08. That lifts the average by less than 0.1.
• (d)
  16.2 — 16.2 is the new average, not the newcomer's age. A 16.2-year-old would move the average only to 656.2 ⁄ 41 ≈ 16.005.

Total = average × count. When one member joins, the newcomer's value is the new total minus the old total.

The shortcut asks what the newcomer must bring: the old average, plus 0.2 for each of the 41 people now in the class, so 16 + 41 × 0.2 = 24.2. Equally, it is the new average plus 0.2 for each of the original 40: 16.2 + 8 = 24.2.

Key facts

• Total = average × number of members.
• Newcomer = old average + (new count × rise) = 16 + 41 × 0.2 = 24.2.
• Newcomer = new average + (old count × rise) = 16.2 + 40 × 0.2 = 24.2.

Common traps

• Adding 40 × 0.2 to the old average: 16 + 8 = 24 starts from 16, but with the old count the base must be the new average, 16.2.
• Choosing 16.2, which is the new average, not the new student's age.

No directly related past PYQ was found.