The average age of 17 boys and their teacher is 16 years When the teacher's age is excluded, the average age decreases by 1 year. The age of the teacher is:

33 years 

The average age of 17 boys and their teacher = 16 years.

Total age of 17 boys and teacher = (17 + 1) × 16

When the teacher’s age is excluded, Total decreased age = 17 × (16 – 1)

The age of the teacher = (17 + 1) × 16 – 17 × (16 – 1)

∴ The age of the teacher = 18 × 16 – 17 × 15 = 288 – 255 = 33 years.