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?

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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.