Question

The average marks scored by the students of a class in mathematics is 75. The average of marks scored by boys and girls are respectively 79 and 59. Find the percentage of boys in the class.

Answer 1

Given:

Overall average = 75.

Average of boys = 79.

Average of girls = 59.

Step-wise calculation:

1. Let total students = N

Number of boys = b

Number of girls = N – b

2. Total marks = 75N

= (Sum of boys’ marks) + (Sum of girls’ marks) 

= 79b + 59(N – b)

3. So, 75N = 79b + 59N – 59b

= 20b + 59N

4. Rearranging: 75N − 59N = 20b

⇒ 16N = 20b

⇒ `b = (16/20)N` 

⇒ `b = (4/5)N`

Fraction of boys = `4/5` = 0.8

Percentage of boys = 80%.