The average score of boys in an examination in a school is 72 and that of the…
2024
The average score of boys in an examination in a school is 72 and that of the girls is 75. The average score of the school is 73.2. The ratio of the number of boys to that of the girls that appeared in the examination is
- A.
3:2
- B.
2:2
- C.
1:2
- D.
4:2
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Correct answer: A
Let the number of boys = b and the number of girls = g.
The overall average score is given by (72b + 75g) / (b + g) = 73.2.
Multiply both sides by (b + g): 73.2(b + g) = 72b + 75g.
Expand: 73.2b + 73.2g = 72b + 75g.
Rearrange terms: 73.2b - 72b = 75g - 73.2g → 1.2b = 1.8g.
Divide both sides by 1.2g: b/g = 1.8/1.2 = 3/2.
Check: (72*3 + 75*2)/5 = (216 + 150)/5 = 366/5 = 73.2.
Answer: 3:2