The average age of 24 boys and their teacher is 15 years When the teacher's age is excluded, the average age decreases by 1 year. The age of the teacher is:

39 years

 The average age of 24 boys and their teacher = 15 years.

Total age of 24 boys and teacher = (24 + 1) × 15

When the teacher’s age is excluded, Total decreased age = 24 × (15 – 1)

The age of the teacher = (24 + 1) × 15 – 24 × (15 – 1)

∴ The age of the teacher = 25 × 15 – 24 × 14 = 375 – 336 = 39 years.