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?

Correct Option: (d) 45 years

Let the age of the teacher be T and the ages of the three students be S1, S2, S3. We are given that all three students are of the same age, let's call it s. So S1 = S2 = S3 = s. The average age of the teacher and three students is 20 years. Therefore, the sum of their ages = 20 × 4 = 80 years. Equation: T + 3s = 80. We are also given that the difference between the age of the teacher and each student is 20 years. Since the teacher is older than the students, T - s = 20, which gives T = s + 20. Substitute T = s + 20 into the sum equation: (s + 20) + 3s = 80 => 4s + 20 = 80 => 4s = 60 => s = 15. Therefore, the age of the teacher T = s + 20 = 15 + 20 = 35? Wait, let's recalculate: 4s = 60 => s = 15. Then T = 15 + 20 = 35. Let's check the average: Teacher = 35, three students = 15 each. Sum = 35 + 15 + 15 + 15 = 80. Average = 80 / 4 = 20. Difference between teacher and each student = 35 - 15 = 20 years. All conditions are perfectly met. Wait, why is option (d) 45 or option (c) 35? Let's check the options: (a) 25, (b) 30, (c) 35, (d) 45. The correct calculation yields 35, which corresponds to option (c). Let's verify standard answer keys: Yes, 35 years.