The mean age of a student is 16. So the sum of ages of the 10 students would be `10xx16 = 160`
Let us say the age of the teacher is x. So with the teacher now we have 11 in the group.
Mean age of gruop = `(160+x)/11`
`19 = (160+x)/11`
`x = 49`
So the teacher's age is 49 years.