Question

The average score of boys in an examination of a school is 71 and of girls is 73. The averages score of school in that examination is 71.8. Find the ratio of the number of boys between number of girls appeared in the examination.

Answer 1

Let `bar"X"_1 and bar"X"_2` be the average scores of boys and girls respectively and `bar"X"` be the average of both boys and girls. Then
`bar"X"_1 = 71, bar"X"_2 = 73, bar"X" = 71·8.`
∴ `bar"X" = ("n"_1 bar"X"_1 + "n"_2 bar"X"_2)/("n"_1 + "n"_2)`
⇒ 71·8 = `("n"_1 xx 71 + "n"_2 xx 73)/("n"_1 + "n"_2)`
⇒ 71·8 (n₁ + n₂) = 71n₁ + 73n₂
⇒ 0·8n₁ = 1·2n₂
⇒  8n₁ = 12n₂
⇒ `("n"_1)/("n"_2) = (12)/(8) = (3)/(2)`
Hence n₁ : n₂ = 3 : 2.