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 \(62.\)