Q. The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?
(a) 25 years
(b) 30 years
(c) 35 years
(d) 45 years
Correct Answer: (c) 35 years
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Average age of a teacher and 3 students
Let’s solve this problem step by step. The average age of a teacher and three students is 20 years. This means that the sum of their ages is 20 * 4 = 80 years.
Since all three students are of the same age and the difference between the age of the teacher and each student is 20 years, we can represent the age of each student as x and the age of the teacher as x + 20.
The sum of their ages is then x + x + x + (x + 20) = 80. Solving for x, we find that x = 15. This means that each student is 15 years old.
Since the teacher’s age is represented as x + 20, we can substitute in our value for x to find that the teacher’s age is 15 + 20 = 35 years.
