Question

Aman’s age is times his son’s age. Ten years ago, he was five times his son’s age. Find their present ages.

Answer 1

Hint: We will start solving this question by assuming the ages of Aman and his son. Assuming the present age of Aman’s son be \[x.\]And then Aman’s present age be \[3x.\]Using this information, we will form a linear equation. And on further solving the equation, we will get the required value of x, and hence, the present ages of both Aman and his son.

Complete step-by-step answer:
Let the present age of Aman’s son be \[x.\] Then, according to the question, Aman’s present age be \[3x.\]
Now ten years ago,
Aman’s age \[ = {\text{ }}3x - 10\]
Aman’s son’s age \[ = {\text{ }}x - 10\]
Now, we have been given that ten years ago, Aman was five times his son’s age.
So, Aman’s age \[ = {\text{ }}5\] (Aman’s son’s age)
On forming linear equation using above information, we get
\[\begin{array}{*{20}{l}}
  {3x - 10{\text{ }} = {\text{ }}5\left( {x - 10} \right)} \\
  {3x - 10{\text{ }} = {\text{ }}5x - 50} \\
  {5x - 3x{\text{ }} = {\text{ }}50{\text{ }}-{\text{ }}10} \\
  {2x{\text{ }} = {\text{ }}40}
\end{array}\]
 $ x = \dfrac{{40}}{2} $
\[x = 20\]
Now, substituting the value of x, to get the present age of Aman and his son, we get
Aman’s age \[ = {\text{ }}3x{\text{ }} = {\text{ }}3\left( {20} \right){\text{ }} = {\text{ }}60{\text{ }}years\]
Aman’s son’s age \[ = {\text{ }}x{\text{ }} = {\text{ }}20{\text{ }}years\]
Thus, Aman’s age and Aman’s son’s age are \[60\] years and \[20\] years respectively.

Note: In this question we are asked to find the present ages, so for that we have assumed their present ages. And in the question, we have been given a condition of \[10\] years ago. So, on co- co-relating condition of present ages and the ages \[10\] years ago, we got our required answer.