Question

The average score of a class of boys and girls in an examinations is A. The ratio of boys and girls in the class is 3 : 1 if the average score of the boys is (A + 1), the average score of the girls is

• A. (A - 1)
• B. (A - 3)
• C. (A + 1)
• D. (A + 3)

Answer 1

Answer: (B)

(A - 3)

Let the number of boys be 3x and the number of girls be x.
Then, total number of students = 4x
Average score of the class = A
$\therefore$ Total score of all the students = 4Ax
Average score of all the boys = A + 1
$\therefore$ Total score of all the boys = 3x (A + 1) = 3Ax + 3x
$\Rightarrow$ Total score of all the girls = 4Ax - 3Ax - 3x = Ax - 3x = (A - 3)x
$\Rightarrow$ Average score of the girls = $\frac{(A-3)x}{x}=(A-3)$