Shortcut Trick Total age of 4 persons (1 teacher + 3 boys) = 4 × 25 = 100 years. Assume each boy's age is B. The teacher is older, so teacher's age = (B + 20). Total sum of ages = B + 20 + 3B = 100 ⇒ 4B + 20 = 100 ⇒ 4B = 80 ⇒ B = 20 years. Teacher's age = 20 + 20 = 40 years. ∴ The correct answer is 40 years. Alternate Method Given: Average age of 1 teacher and 3 boys = 25 years. Difference between the teacher's age and each boy's age = 20 years. Formula Used: Total Sum = Average × Number of Persons Age Distribution (Total = 100 years) Teacher B + 20 Boy B Boy B Boy B Total Age = (B + 20) + B + B + B = 100 4B + 20 = 100 → B = 20, Teacher = 40 Calculations: ⇒ Number of people in the group = 1 Teacher + 3 Boys = 4 persons ⇒ Total sum of their ages = 25 × 4 = 100 years ⇒ Let the age of each boy be B years. ⇒ Naturally, the teacher is older, so the age of the teacher = (B + 20) years. ⇒ Total age = Age of Teacher + Age of 3 boys ⇒ 100 = (B + 20) + 3B ⇒ 100 = 4B + 20 ⇒ 4B = 80 ⇒ B = 20 years ⇒ Age of the teacher = B + 20 = 20 + 20 = 40 years ∴ The correct answer is 40 years. Related Concepts: Average of a Group The sum of all observations divided by the total number of observations. Can be quickly calculated as: Sum = Average × Count. Combined Average If group 1 has N_(1) items with average A_(1), and group 2 has N_(2) items with average A_(2), then Combined Average = (N_(1)A_(1) + N_(2)A_(2)) ÷ (N_(1) + N_(2)). Age Problems Rule The age difference between two individuals always remains constant regardless of the number of years passed. In teacher-student problems, the teacher's age is consistently assumed to be greater than the students' age unless specified otherwise.