The average score of boys in an examination in a school is 70 and that of the…
2024
The average score of boys in an examination in a school is 70 and that of the girls is 74. The average score of the school is 72.6. The ratio of the number of boys to that of the girls that appeared in the examination is
- A.
3:7
- B.
5:12
- C.
7:13
- D.
4:9
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Show answer & explanation
Correct answer: C
Key idea: use a weighted average equation where the combined average equals the total marks divided by total students.
Let the number of boys be x and the number of girls be y.
Total marks = 70x + 74y.
Combined average equation: (70x + 74y) / (x + y) = 72.6.
Multiply both sides: 70x + 74y = 72.6x + 72.6y.
Rearrange: -2.6x + 1.4y = 0, so 1.4y = 2.6x and x/y = 1.4/2.6 = 14/26 = 7/13.
Answer: The ratio of the number of boys to girls is 7:13.