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 \[ = {\text{ }}7\] 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 \[ = {\text{ }}\left( {x + 7} \right)\] years
According to this question:
$\begin{array}{*{20}{c}}
  { \Rightarrow \left( {x + 7} \right) = \dfrac{{\left( {x + 35} \right)}}{2}} \\
  { \Rightarrow 2\left( {x + 7} \right) = \left( {x + 35} \right)} \\
  { \Rightarrow 2x + 14 = x + 35} \\
  {\therefore x = 21}
\end{array}$
After \[21\]years:
Age of man \[ = {\text{ }}\left( {x{\text{ }} + {\text{ }}35} \right){\text{ }} = {\text{ }}\left( {21 + 35} \right){\text{ }} = {\text{ }}56\] years
Age of son \[ = {\text{ }}\left( {x + 7} \right){\text{ }} = {\text{ }}\left( {21 + 7} \right){\text{ }} = {\text{ }}28\] 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.