Correct Answer - Option 4 : 63
Given:
Average score of 84 students = 57
Ratio of boy and Girl = 10 ∶ 11
Average score of boys = (80/100) × Average score of girls
Formula used:
Average on 'n' numbers = (Sum of 'n' numbers)/n
sum of 'n' numbers = (Average on 'n' numbers) × n
Calculation:
The Total marks scored by 84 students = 84 × 57
= 4788
Let the Number of boys and girls = 10x and 11x
∵ The total number of students = 84
∴ 10x + 11x = 84
⇒ 21x = 84
⇒ x = 84/21
⇒ x = 4
Number of Boys = 10x = 10 × 4 = 40
Number of Girls = 11x = 11 × 4 = 44
Average score of boys = (80/100) × Average score of girls
⇒ (Average score of boys) ∶ (Average score of girls) = 4 ∶ 5
Let the Average score of boys = 4y
Average score of girls = 5y
Total marks scored by 40 boys = 40 × (4y)
= 160y
Total marks scored by 44 girls = 44 × (5y)
= 220y
∵ Total marks scored by 40 boys + Total marks scored by 44 girls = Total marks scored by 84 students
∴ 160y + 220y = 4788
⇒ 380y = 4788
⇒ y = 4788/380
⇒ y = 12.6
Average score of 44 girls = 5y
= 5 × 12.6
= 63
