Question

The average age of 14 girls and their and teacher's age is 15yr. If teachers age is excluded, then the average reduced by 1. What is teacher's age?

Answer 1

Sum of ages of all girls = X

Age of the teacher = Y

We know that average age of all girls = X ÷ 14.

And, average age of the girl's ages and teacher's age = 15

We know that average age of all girls is 1 year less that average age when the teacher is also included.

So we can then write this as :

(X + Y ) ÷ 15 = 15 (Since we are taking average age of 15 people, we divide by 15).

or X + Y = 15 * 15 = 225

or X = 225 - Y

Average age of all girls = X * 14 (Sum of ages of the girls divided by number of girls).

We also know that this value is 1 less that the average age of girls + teacher.

Therefore, X ÷ 14 = 14, or (225 - Y) = 196

Which means, Y = 225 - 196 = 29

And X = 225 - Y = 196 (Sum of ages of all girls)