The sum of digits of a two-digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?

Given:

The sum of digits of a two-digit number is 13.

If the number is subtracted from the one obtained by interchanging the digits, the result is 45. 

 To do:

We have to find the number.

Solution:

Let the two-digit number be $10x+y$.

According to the question,

$x+y=13$-----(i)

The number obtained on reversing the digits is $10y+x$.

$10y+x-(10x+y)=45$

$10y-y+x-10x=45$

$9y-9x=45$

$9(y-x)=45$

$y-x=5$

$y=5+x$

Substituting the value of $y$ in equation (i), we get,

$x+(5+x)=13$

$2x+5=13$

$2x=13-5$

$2x=8$

$x=4$

This implies,

$y=5+4=9$

$10x+y=10(4)+9=40+9=49$

The required number is 49.  

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

293 Views

Kickstart Your Career

Get certified by completing the course

Get Started