Question

Amit is now 6 times as old as his son. Four years from now, the sum of their ages will be $43$ years. Determine Amit’s present Age.

Answer 1

Hint: We will assume the present age of Amit’s son as $x$ years. Then from the given data we will find the present age of Amit and equates it to another variable $y$. Now from the given statement, we will find the ages of Amit and his son after Four years, then we will establish an equation involving the variables Amit and his son age. We will solve the equation to get the age of Amit.

Complete step-by-step solution:
Let the present age of Amit’s son is $x$ years, then age of Amit is $6$ times than his son, so the age of Amit is
$y=6x$
After Four years
Age of Amit’s son is $x+4$ years
Age of Amit is $y+4=6x+4$
Given that, the sum of their ages after Four years is $43$. Then
$\begin{align}
  & x+4+y+4=43 \\
 &\Rightarrow x+4+6x+4=43 \\
 &\Rightarrow 7x=43-8 \\
 &\Rightarrow 7x=35 \\
 &\Rightarrow x=5
\end{align}$
So, the age of Amit son is $x=5$ years then the age of Amit is
$\begin{align}
  & y=6x \\
 & =6\left( 5 \right) \\
 & =30
\end{align}$
Hence the age of Amit is $30$years.

Note: For this kind of problem understand the question language and declare the variables which are necessary. By taking the given statements into consideration form an equation. You can also use the table format to solve the question in a better way.

Name	Present Age	Age after $4$years
Amit’s Son	Let $x$	$x+4$
Amit	$6x$(from given data)	$6x+4$

In the problem then mentioned that the sum of ages after $4$ years is $43$. Then
$\begin{align}
  & x+4+6x+4=43 \\
 & 7x=43-8 \\
 & x=\dfrac{35}{7} \\
 & x=5
\end{align}$
So, the present age of Amit’s son is $5$years, so the age of Amit is $6\left( 5 \right)=30$years.
From both the methods we got the same answer.