# EX.2.2 Q5 Linear Equations in One Variable Solutions - NCERT Maths Class 8

## Question

Two numbers are in the ratio \(5:3\). If they differ by \(18\), what are the numbers?

## Text Solution

**What is known?**

(i) Two number are in ratio \(5:3\).

(ii) They differ by \(18\).

**What is unknown?**

Number

**Reasoning:**

Assume any one number to be a variable and form a linear equation by using the relationships between the two numbers as mentioned in the problem statement. Any one relationship will allow you to express one number in terms of the other number (assumed to be a variable first). Then, the second relationship will allow you to form a linear equation.

**Steps:**

Two number are in ratio \(5:3\)

\(\therefore \)The number are \(5x\) and \( 3x\)

The two numbers differ by \( 18\):

\[5x - 3x = 18\]

\[\begin{align}2x &= 18\\x &= 9\end{align}\]

First number is \(5x = 5 \times 9 = 45\)

Second number is \(3x = 3 \times 9 = 27\)

The numbers will be \(45\) and \( 27\).