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 4 members age (A=25, N=4)

⇒S=25 X 4 =100

Later, Head of the family included, Average increases by 20% (so A=30, N=5)

So, sum of 5 members age 

⇒S=30 X 5 =150-100

Now,

The age of the head =(sum of 4 members age)-(Sum of 5 members age)

=150-100

=50 yr.

Hence, Option B is correct.