### Solution:

Given that the sum of age of 2 daughters and one son is equal to the age of father and after 15 years sum of ages of children will be $1\frac{1}{2}$ times the age of father.Let the present age of the father be x years and that of sum of all his children be y years.

According to the first condition,

$\Rightarrow x=y$……..(1)

Since the man has three children, so according to the second condition,

$\Rightarrow 1\frac{1}{2}(x+15)=y+15\times \left(3\right)$ ……(2)

Substituting y for x into equation 2,

$\Rightarrow 1.5(y+15)=y+15\times \left(3\right)$ $\Rightarrow 1.5y+22.5=y+45$ $\Rightarrow 0.5y=22.5$

$\Rightarrow y=45$

Substituting 45 for y into equation 1,

$\Rightarrow x=45$

Therefore, the present age of the father is 45 years.

Hence, option (1) is correct.