Explanation:

Sol. Ans.(c).

Traditional Method Let the age of Teachers is T years and the three students is a years (Given age of all three student is same). Then according to the information given in question we have (T + 3a)/4 = 20 or T + 3a = 80 ….(1)

T – a = 20 ….(2) (assuming that teachers age will be greater than the students)

By solving equations 1 and 2 simultaneously we have a = 15 and T = 35. Option (c) is correct.

Working backward from options method:

Option (a) – If teacher’s age is 25 years, then students’ age would be 5 years (assuming that teachers age will be greater than the students). This will give average of teacher and students age to (25 + 3×5)/4 = 10. Hence it is not correct.

Option (b) – If teacher’s age is 30 years, then students age would be 10 years (assuming that teachers age will be greater than the students). This will give average of teacher and students age to (30 + 3×10)/4 = 15 .Hence it is not correct.

Option (c) – If teacher’s age is 35 years, then students age would be 15 years (assuming that teachers age will be greater than the students). This will give average of teacher and students age to (35 + 3×15)/4 = 20. This matches the information given in question. Hence it is the correct answer.

No need to check option (d).