Question

Father's age is three times the sum of ages of his two children. After $5$ years, his age will be twice the sum of the ages of two children. Find the age of the father.

Answer 1

Step 1: Given

Let father's present age be denoted as $x$ and the present age of the two sons be denoted as $y$ and $z$ in years

Father's present age, $x=3(y+z)$

After $5$ years, $x+5=2(y+5+z+5)$

Step 2: Finding the value of $(y+z)$

We know that $x=3(y+z)$

Substituting the value of $x$ above equation,

$$\begin{gathered} 3(y+z)+5=2(y+z+10) \\ \Rightarrow 3y+3z+5=2y+2z+20 \\ \Rightarrow y+z=15 \end{gathered}$$

Therefore, the sum of the age of the two sons is $15$ years

Step 3: Substituting the value of $(y+z)$ in the first equation

$$\begin{gathered} x=3(y+z) \\ \Rightarrow x=3·15 \\ \Rightarrow x=45 \end{gathered}$$

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