The average score of boys in an examination at a school is 71, and that of…
2025
The average score of boys in an examination at a school is 71, and that of girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls who appeared in the examination.
- A.
3:2
- B.
3:7
- C.
5:12
- D.
4:9
Attempted by 15 students.
Show answer & explanation
Correct answer: A
Solution: Use a weighted average equation to find the ratio of numbers.
Let the number of boys be b and the number of girls be g.
The combined average satisfies (71b + 73g)/(b + g) = 71.8.
Multiply both sides: 71b + 73g = 71.8b + 71.8g.
Rearrange terms: (71 - 71.8)b + (73 - 71.8)g = 0 → -0.8b + 1.2g = 0.
Solve for the ratio: 1.2g = 0.8b → divide by 0.4 → 3g = 2b → b:g = 3:2.
Quick check: the combined average 71.8 is closer to the boys' average 71 than to 73, so there are more boys; ratio 3:2 matches that intuition.
Therefore, the ratio of the number of boys to the number of girls is 3:2.