Question

A man is $$35$$ years old and his son $$7$$years now. In how many years will the son be half as old as his father?

Answer 1

Hint: To solve this problem, we will assume that after x years, the son will be half as old as his father.That is,we are taking the unknown quantity as x.


Complete step by step solution:
We are given that:
The age of a man in $$35$$ years and that of his son in $$7$$years.
Now we need to find that,
After how many years will the son be half old as his father.
Age of man-years
Age of his son $$=7$$ years
Let after x years the son’s age become half of that of father.
Hence, age after x years.
Age of man-years
Age of his son $$=\left(x+7\right)$$ years
According to this question:
$\begin{array}{c}\Rightarrow \left(x+7\right)={\displaystyle \frac{\left(x+35\right)}{2}}\\ \Rightarrow 2\left(x+7\right)=\left(x+35\right)\\ \Rightarrow 2x+14=x+35\\ \therefore x=21\end{array}$
After $$21$$years:
Age of man $$=\left(x+35\right)=\left(21+35\right)=56$$ years
Age of son $$=\left(x+7\right)=\left(21+7\right)=28$$ years
So, after $$21$$years he will be half of his father’s age.


Note: We assumed their ages after x years then simply equate the equation according to question and calculated x i.e. how many years.