Question

Let the average score of a class of boys and girls in an examination be p. The ratio of boys and girls in the class is 3 ∶ 1. If the average score of the boys is (p + 1), then what is the average score of the girls?
1. (p - 1)
2. (p - 2)
3. (p - 3)
4. p

Answer 1

Correct Answer - Option 3 : (p - 3)

Given:

Let the average score of a class of boys and girls in an examination be p. The ratio of boys and girls in the class is 3 ∶ 1. If the average score of the boys is (p + 1),

Calculation       

Let the number of boys be 3x and number of girls x

Let the average score of the girls be q

Sum of score of boys = 3x (p + 1)

Sum of score of girls = qx

Sum of score of the whole class = (3x + x)p = 4xp

According to question,

3x (p+1) + qx = 4xp

3xp + 3x + qx = 4xp

x(3 + q) = xp

3 + q = p

Then, q = (p – 3)

Hence, average score of the girls = (p - 3)