Given:
Average score of the class = 56
Average score of the brightest 25% students = 80
Average score of the dullest 35% students = 30
Ratio of boys and girls in the remaining 40% = 2:3
Average score of boys in the remaining 40% = 60
Formula Used:
Total average score = (Sum of scores of all students) / (Total number of students)
Average score = (Sum of scores in a group) / (Number of students in that group)
Calculation:
Let the total number of students = 100 (assume for simplicity).
⇒ Number of brightest 25% students = 25
⇒ Sum of scores of brightest 25% students = 25 × 80 = 2000
⇒ Number of dullest 35% students = 35
⇒ Sum of scores of dullest 35% students = 35 × 30 = 1050
⇒ Number of remaining 40% students = 40
⇒ Total sum of scores of all students = 100 × 56 = 5600
⇒ Sum of scores of remaining 40% students = 5600 - (2000 + 1050) = 2550
Let the number of boys in the remaining 40% = 2x and girls = 3x (ratio 2:3).
⇒ 2x + 3x = 40
⇒ x = 8
⇒ Number of boys = 2x = 16
⇒ Number of girls = 3x = 24
⇒ Sum of scores of boys = 16 × 60 = 960
⇒ Sum of scores of girls = Total sum of scores of remaining 40% - Sum of scores of boys
⇒ Sum of scores of girls = 2550 - 960 = 1590
⇒ Average score of girls = (Sum of scores of girls) / (Number of girls)
⇒ Average score of girls = 1590 / 24 = 66.25
∴ The correct answer is 66.25.