Question

The ages of Rahul and Haroon are in the ratio of 3:5. Seven years later the sum of their ages will be 62 years. What are their present ages?

Answer 1

Hint: In this problem, we need to find out the expression for the ages of the Rahul and Haroon in a single variable. Then, add their ages and equate with 62.

Completes step-by-step solution -
Since the ages of Rahul and Haroon are in the ratio of $3:5$, consider, the age of Rahul be $3x$, and the age of Haroon be $5x$.
After seven years, the ages of Rahul and Haroon is as follows:
$\begin{align}
  {\text{Rahul's age}} = 3x + 7 \\
  {\text{Haroon's age}} = 5x + 7 \\
\end{align}$
Since the sum of the ages of the Rahul and Haroon after seven years is 62 years, it can be written as shown below.
 $\left( {3x + 7} \right) + \left( {5x + 7} \right) = 62 \\$
 $\Rightarrow 3x + 7 + 5x + 7 = 62 \\$
 $\Rightarrow 8x + 14 = 62 \\$
 $\Rightarrow 8x = 62 - 14 \\$
 $\Rightarrow 8x = 48 \\$
 $\Rightarrow x = 6 \\ $
The present age of the Rahul is calculated as shown below.
$\begin{align}
  {\text{Rahul's age}} = 3\left( 6 \right) \\
  {\text{Rahul's age}} = 18 \\
\end{align}$
The present age of the Haroon is calculated as shown below.
$ {\text{Haroon's age}} = 5\left( 6 \right) \\$
 ${\text{Haroon's age}} = 30 \\ $
Thus, the present age of Rahul is 18 years and the present age of Haroon is 30 years.

Note: In this problem, obtain the ages of Rahul and Haroon in a single variable. Sometimes students let the ages in two variables and form the equations in two variables it becomes tough to find the value of both variables. So students should try to keep equations in a single variable.