# Ex.2.4 Q4 Linear Equations in One Variable Solution - NCERT Maths Class 8

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## Question

One of the two digits of a two-digit number is three times the other digit. If you interchange the digit of this two-digit number and add the resulting number to the original number, you get $$88$$. What is the original number?

Video Solution
Linear Equations
Ex 2.4 | Question 4

## Text Solution

What is known?

i) One of the two digits of a two-digit number is three times the other digit

ii) Interchanging the digit of this two-digit number and adding the resulting number to the original number results in $$88$$.

What is unknown?

Original number

Reasoning:

Assume one of the digits of two-digit as variable then use other conditions and form a linear equation.

Steps:

Let the digits at tens place and ones place be $$x$$ and $$3x$$ respectively.

Therefore, original number $$= 10x + 3x = 13x$$

On interchanging the digits, the digits at ones place and tens place will be $$x$$ and $$3x$$ respectively.

Number after interchanging $$= 10 \times 3x + x = 30x + x = 31x$$

According to the given question,

Original number $$+$$ New number $$=$$ $$88$$

\begin{align}{13x + 31x = 88} \\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,44x = 88}\end{align}

Dividing both sides by $$44$$, we obtain

$x = 2$

Therefore, original number $$= {\text{ }}13x = 13 \times 2 = 26$$

By considering the tens place and ones place as 3$$x$$ and $$x$$ respectively, the two-digit number obtained is $$62.$$

Therefore, the two-digit number may be $$26$$  or $$62.$$

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