# Ex.2.4 Q2 Linear Equations in One Variable Solution - NCERT Maths Class 8

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## Question

A positive number is $$5$$ times another number. If $$21$$ is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Video Solution
Linear Equations
Ex 2.4 | Question 2

## Text Solution

What is known?

i) A positive number is $$5$$ times another number

ii) $$21$$ is added to both the numbers

iii) Then one of the new numbers becomes twice the other new number

What is unknown?

Numbers

Reasoning:

Assume one positive number to be variable then use the conditions to form a linear equation.

Steps:

Let the numbers be $$x$$ and $$5x$$. According to the question,

\begin{align}21 + 5x &= 2\left( {x{\text{ }} + {\text{ }}21} \right) \\21 + 5x &= 2x{\text{ }} + {\text{ }}42\end{align}

Transposing $$2x$$ to LHS and $$21$$ to RHS, we obtain

\begin{align}5x - 2x &= 42 - 21 \\3x &= 21\end{align}

Dividing both sides by $$3$$, we obtain

$x = 7$

First number is $$\,x=7$$

Second number is $$5x = {\text{ }}5 \times 7 = 35$$

Hence, the numbers are $$7$$ and $$35$$ respectively.

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