Average weight of boys in a class is 55 kg while average weight of girls in…
2022
Average weight of boys in a class is 55 kg while average weight of girls in the same class is 35 kg. If the average of all the students in the class is 40 kg, find the ratio of boys and girls in the class.
- A.
3 : 1
- B.
2 : 3
- C.
1 : 3
- D.
3 : 2
Show answer & explanation
Correct answer: C
Concept
When two groups are combined, the overall (weighted) average lies between the two group averages. The rule of alligation states that the two groups split in the inverse ratio of their distances from the overall average:
(number in group 1) : (number in group 2) = (distance of group 2's average from the mean) : (distance of group 1's average from the mean).
Application
Boys' average = 55 kg, girls' average = 35 kg, overall average = 40 kg. Let the number of boys be b and girls be g.
Total weight equation: 55b + 35g = 40(b + g).
Expand the right side: 55b + 35g = 40b + 40g.
Collect like terms: 55b − 40b = 40g − 35g, so 15b = 5g.
Divide both sides by 5: 3b = g, hence b : g = 1 : 3.
Cross-check (alligation)
Distance of boys' average from the mean = 55 − 40 = 15; distance of girls' average from the mean = 40 − 35 = 5. By alligation, boys : girls = 5 : 15 = 1 : 3, which matches.
So boys : girls = 1 : 3.