Question

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

Answer 1

Hint:
Here, we need to find the present ages of Rahul and Haroon. We will consider the present ages of Rahul and Haroon in terms of \[x\] and then we will find their ages 4 years later. Then, we will form an equation as per the question to find the value of \[x\]. Subsequently, we will find their present ages by using the value of \[x\].

Complete step by step solution:
Let the present age of Rahul and Haroon be \[5x\] and \[7x\] respectively.
The ages of Rahul and Haroon 4 years later will be 4 more than their present ages.
Thus, we get the ages of Rahul and Haroon 4 years later as \[5x + 4\] and \[7x + 4\] respectively.
Now, we know that the sum of ages of Rahul and Haroon 4 years later will be equal to 56.
Thus, we get the equation
\[\left( {5x + 4} \right) + \left( {7x + 4} \right) = 56\]
Adding the like terms on the left hand side of the equation, we get
\[12x + 8 = 56\]
Now, we will subtract 8 from both sides of the equation.
\[\begin{array}{l}12x + 8 - 8 = 56 - 8\\12x = 48\end{array}\]
Dividing both sides by 12, we get the value of \[x\] as
\[\begin{array}{l}\dfrac{{12x}}{{12}} = \dfrac{{48}}{{12}}\\x = 4\end{array}\]
We can find the present ages of Rahul and Haroon by substituting the value of \[x\] in the expressions \[5x\] and \[7x\].
Substitute 4 for \[x\] in the expressions \[5x\] and \[7x\], we get

Present age of Rahul \[ = 5x = 5 \times 4 = 20\] years
Present age of Haroon \[ = 7x = 7 \times 4 = 28\] years

Note:
We can verify our answer by checking the ratio of the present ages of Rahul and Haroon, and the sum of their ages four years later. The present ages of Rahul and Haroon are in the ratio \[20:28 = 5:7\] years. The ages of Rahul and Haroon 4 years later are 24 and 32 respectively. The sum of 24 and 32 is 56. Hence, we have verified that our answer is correct.