Average age of 20 students of a class is 10 years. Average age of these students together with their five teachers is 14. The age of Ramesh Sir, one of their five teachers, is exactly the same as the average age of all their five teachers. The sum of the ages (in years) of all the students and Ramesh Sir is

Correct option is C

Given:
Average of 20 students = 10 years => Sum of students = 20 × 10 = 200.
Average of (20 students + 5 teachers) = 14 => Total sum (students + 5 teachers) = 25 × 14 = 350.
Formula:
Required sum = (Sum of students) + (Age of Ramesh) = 200 + 30.

Solution:

Sum of ages of 5 teachers = 350 − 200 = 150.
Ramesh's age = average age of the 5 teachers = 150 / 5 = 30.

200 + 30 = 230.

Correct Answer: (c) 230