In a school, 20% of the students are aged 8 years, 50% of the remaining students are of 10 years of age and the remaining students are of 15 years of age. What is the percentage of the average age of the students to the average age to the teachers which is 25 years?

Correct option is A

1. Students aged 8 years: 20% of the students are 8 years old.
2. Remaining students: 100% - 20% = 80% of the students remain.
3. Students aged 10 years: 50% of the remaining students are 10 years old. So, 50% of 80% = 0.50 x 80% = 40% of the total students are 10 years old.
4. Students aged 15 years: The remaining students are 15 years old. The percentage of these students is: 100% - 20% - 40% = 40%.
5. Calculate the average age of the students:
· Let the total number of students be 100.
· Number of 8-year-old students = 20
· Number of 10-year-old students = 40
· Number of 15-year-old students = 40
· Total age of students = (20 x 8) + (40 x 10) + (40 x 15) = 160 + 400 + 600 = 1160
· Average age of students = 1160 / 100 = 11.6 years.
6. Calculate the percentage of the average age of students to the average age of teachers:
· Average age of teachers = 25 years.
· Percentage = (Average age of students / Average age of teachers) x 100
· Percentage = (11.6 / 25) x 100 = 0.464 x 100 = 46.4%
Therefore, the percentage of the average age of the students to the average age of the teachers is 46.40%.