In a class of 150 students (boys and girls only), the girls are 60. The average weight of boys is 52 kg and that of girls is 48 kg. What is the average weight (in kg) of the whole class?

Correct — D. Boys = 150 − 60 = 90.

Boys' total weight = 90 × 52 = 4680 kg
Girls' total weight = 60 × 48 = 2880 kg
Class total = 4680 + 2880 = 7560 kg

Class average = 7560 ⁄ 150 = 50.4 kg → option (d).

Why the others are wrong

• (a)
  48.8 — 48.8 is the mean you get when the heavier group is only 30 of the 150. There are 90 boys at 52 kg, so the class mean must sit well above the halfway 50.
• (b)
  49.6 — 49.6 is the counts swapped: 90 girls at 48 and 60 boys at 52 gives 7440 ⁄ 150 = 49.6. The question puts the 60 on the girls.
• (c)
  51.2 — 51.2 is the mean of a 4 : 1 boys-to-girls split. This class splits 90 : 60, that is 3 : 2, so the mean is 48 + (3⁄5) × 4 = 50.4.

This is a weighted average, also called a mixture or alligation problem. The combined mean of two groups is not the average of their two means unless the groups are the same size.

Written as alligation, the mean splits the gap between 48 and 52 in the ratio of the counts. Boys are 90 of 150, so the mean sits 3⁄5 of the way up from 48: 48 + (3⁄5) × 4 = 50.4.

Both routes give the same number. The alligation route is faster when the options are spread out, because it tells you which side of 50 the answer falls on before any multiplication.

Key facts

• Weighted mean = (n1x1 + n2x2) ⁄ (n1 + n2), not (x1 + x2) ⁄ 2.
• By alligation the combined mean divides the gap between the two means in the ratio of the counts.
• The plain average of 52 and 48 is 50, and the class mean 50.4 sits above it because boys outnumber girls.
• Total class weight here is 7560 kg across 150 students.

Common traps

• Averaging 52 and 48 to 50 and picking the nearest option.
• Taking the 60 as the number of boys.
• Assuming a class of 150 splits evenly rather than computing 150 − 60.

No directly related past PYQ was found.