# EX.2.2 Q9 Linear Equations in One Variable Solutions - NCERT Maths Class 8

## 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?

## Text Solution

**What is known?**

(i) Ages of Rahul and Haroon are in ratio \(5 :7\)

(ii) Four years later, sum of their ages will be \(56\) years.

**What is unknown?**

Present ages of Rahul and Haroon.

**Reasoning:**

Assume the age of either Rahul or Haroon as a variable. Use the first condition to express the ages in terms of the variable. Then use the second condition to form a linear equation.

**Steps:**

Ages of Rahul and Haroon are in ratio \(5 :7\)

Present ages of Rahul and Haroon are \(5x\) and \(7x\) respectively.

Four years later, sum of their ages will be \(56 \) years.

Four years later, age of Rahul \( = 5x + 4\)

Four years later, age of Haroon \( = 7x + 4\)

Sum ➔\(5x + 4 + 7x + 4 = 56\)

\[\begin{align}12x + 8 &= 56\\12x &= 56 - 8\\12x &= 48\\x &= \frac{{48}}{{12}}\\x &= 4\end{align}\]

Present age of Rahul \( = 5x = 5 \times 4 = 20\)

Present age of Haroon \( = 7x = 7 \times 4 = 28\)

Present age of Rahul and Haroon are \( 20 \) and \(28\) years respectively.