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 5 boys age (A=16, N=5)

⇒S=16 X 5 =80

Later, Average decreased by 1 and number of observations increased by 1 (so A=11, N=7)

So, sum of ages of 4 boys

⇒S=16.25 X 4 =65

Now,

Th age of 5th boy =(sum of 5 boys age)-(Sum of age of 4 boys)

=80-65

=15 yr.

Hence, Option A is correct.