Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of 15 members age (A=15, N=15)

⇒S=15 X 15 =225

Later, the teachers age is excluded, the average reduced by 1 yr. (so A=14, N=14)

So, sum of 14 girls age

⇒S=14 X 14 =196

Now,

The Teacher's age =(sum of 15 members age)-(Sum of 14 girls age)

    =225-196

    =29 yr.

Hence, Option A is correct.