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Correct option is B)

Let the age of father $=x$ years

The sum of the age of $2$ children $=y$ years

According to the first condition

$⇒x=3y.....eq1$

After $5$ years

$⇒$ Father's age $=x+5$

$⇒$ The sum of ages of his two children $=y+10$

According to the second condition

$⇒x+5=2(y+10)⇒x+5=2y+20$

$⇒x−2y=15....eq2$

Put the value of $x$ from $eq1$

$⇒3y−2y=15⇒y=15$

Put $y=15$ in $eq1$

$⇒x=3×15⇒x=45$

Hence, father age $=45$ years

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