Question

The age of a father is $35$ years more than thrice of his son's age . After $10$ years, father's age will be $10$ years less than four times the age of his son. Find the age of son and father

Answer 1

Here given that ,

Age of father is $35$ years more than thrice of his son's age.

i.e- Let the age of son is $x$

then age of father is $3x+35$

After $10$ years Age of son will be $x+10$

then, age of father will be $3x+35+10=3x+45$

Then. father's age will be $10$ years less than four times the age of his son.

According to the question,

$$\begin{gathered} 3x+45=4(x+10)-10 \\ \Rightarrow 3x+45=4x+40-10 \\ \Rightarrow 3x-4x=30-45 \\ \Rightarrow -x=-15 \\ \Rightarrow x=15 \end{gathered}$$

So, the age of son is $x=15$ years and father's age is $3x+35=3\times 15+35=45+35=80$ years

Hence, the age of son is $15$ years and age of father is $80$ years