Question

The average score of a class of boys and girls in an examination 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 is: (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 

∴ Total score of all the students = 4Ax 

Average score of all the boys = A + 1

∴ Total score of all the boys = 3x (A + 1) = 3Ax + 3x 

⇒ Total score of all the girls = 4Ax – 3Ax – 3x = Ax – 3x = (A – 3)x 

⇒Average score of the girls =\(\frac{(A-3)x}{x}\) = (A – 3).