In a class of 75 students, there are 35 girls and the rest are the boys. During the science class test, the total marks scored by the boys is 30 more than the total marks scored by the girls. The average marks of the class are 23.6 excluding 6 boys and 4 girls who were not present on the day of the test. What are the average marks scored by the boys?

Option 1 : 23

Total number of students = 75

Number of girls in class = 35

Number of boys = Total students – number of girls = 75 – 35 = 40

Number of students who attempted the test = 75 – 6 – 4 = 75 – 10 = 65

Total marks scored by 65 students = 65 × average marks of students = 65 × 23.6 = 1534

Let's assume the total marks scored by boys = x and the total marks scored by the girls = y

Total marks scored by students = x + y

⇒ x + y = 1534     ----(1)

From the condition given in the question,

Total marks of boys = total marks of girls + 30

⇒ x = y + 30     ----(2)

Substitute the value of x from equation 2 in equation 1.

⇒ y + 30 + y = 1534

⇒ 2y + 30 = 1534

⇒ y = 1504/2 = 752

Substitute the value of y in equation 2.

Total marks scored by boys = 752 + 30 = 782

Number of boys who attempted the exam = 40 – 6 = 34