A class of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 72. What is the average score of the class?

Correct — B. The two groups are different sizes, so this is a weighted average: total the marks first, divide once at the end.

Group 1: 12 students × 62 = 744
Group 2: 30 − 12 = 18 students × 72 = 1,296

Class total = 744 + 1,296 = 2,040
Class average = 2,040 ⁄ 30 = 68 → option (b)

Faster route (alligation): start at the lower mean and step up by the bigger group's share of the 10-mark gap.
62 + (18⁄30) × 10 = 62 + 6 = 68

Why the others are wrong

• (a)
  67 — 67 is the plain mean of 62 and 72. That would be right only if the two groups were both 15 strong; the larger group of 18 sits at 72 and drags the class average above the midpoint.
• (c)
  66 — 66 is below the midpoint 67, which is impossible here. More students score 72 than 62, so the class average must land above 67, never below it.
• (d)
  69 — 69 overshoots. The gap between the group means is 10 and 18 of the 30 students sit at the top, so the rise above 62 is (18⁄30) × 10 = 6, not 7.

A weighted average is the total of everything divided by the count of everything. Two group means cannot simply be averaged unless the groups are the same size.

Two safe routes reach 68. Sum the marks, 12 × 62 + 18 × 72 = 2,040, and divide by 30. Or use alligation: begin at the smaller mean and add (bigger group ⁄ total) × (difference of means).

Alligation also hands you a sanity check before any arithmetic. The answer must lie strictly between 62 and 72, and closer to 72 because more students sit there.

Key facts

• Weighted average = sum of all values ÷ total count, not the mean of the group means.
• 12 × 62 = 744 and 18 × 72 = 1,296, giving 2,040 marks over 30 students.
• By alligation, the class mean is 62 + (18⁄30) × (72 − 62) = 68.
• A weighted mean always lies strictly between the two group means it combines.

Common traps

• Averaging 62 and 72 to get 67, which throws away the group sizes.
• Reading 12 as the size of the higher-scoring group instead of the lower.
• Dividing 2,040 by 12 or by 18 rather than by the full 30.

No directly related past PYQ was found.