The ages of Rahul and Haroon are in the ratio of $5 : 7$ . Four years later the sum of their ages will be $56$ years. What are their present ages?

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Solution

Step 1. Form the equation with the given information.
The given ratio of ages of Rahul and Haroon is $5 : 7$ .
Take the ages of Rahul and Haroon as $5 x$ and $7 x$ .
Their ages after 4 years will be $5 x + 4$ and $7 x + 4$ , the given sum of their ages after $4$ years is $56$ years.
Therefore,
$\begin{array}{rcl} (5 x + 4) + (7 x + 4) & = & 56 \\ \Rightarrow & 5 x + 4 + 7 x + 4 = 56 \\ \Rightarrow & 12 x + 8 = 56 \\ \Rightarrow & 12 x = 56 - 8 \\ \Rightarrow & 12 x = 48 \\ \Rightarrow & x = \frac{48}{12} \\ \Rightarrow & x = 4 \end{array}$
Step 2. Determine the present ages of Rahul and Haroon.
Put the derived value $x = 4$ in $5 x$ and $7 x$
Rahul's present age is calculated as follows:
$\begin{array}{rcl} 5 x & = & 5 \times 4 \\ \Rightarrow & 5 x = 20 \end{array}$
Haroon's present age is calculated as follows:
$7 x = 7 \times 4 \Rightarrow 7 x = 28$
Therefore, the present ages of Rahul and Haroon are $20$ years and $28$ years respectively.

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