The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?

Given :

The digits of a two-digit number differ by 3.

If the digits are interchanged and the resulting number is added to the original number, we get 143.

To do :

We have to find the original number.

Solution :

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

$x-y=3$ or $y-x=3$

If the digits are interchanged and the resulting number is added to the original number, we get 143.

This implies,

$(10x+y)+(10y+x) = 143$

$10x+x+10y+y=143$

$11x+11y=143$

$11(x+y)=143$

$x+y=\frac{143}{11}$

$x+y=13$

If $x-y=3$,

$x+y=13$

$x-y+x+y=3+13$

$2x=16$

$x=8$

$8+y=13$

$y=13-8=5$

$x = 8, y=5$

Then the original number is $10x+y=10(8)+5=85$

If $y-x=3$,

$x+y=13$

$y-x+x+y=3+13$

$2y=16$

$y=\frac{16}{2}$

$y=8$

$x+8=13$

$x=13-8=5$

Then the original number is $10x+y=10(5)+8$=58

Therefore, the original number is 85 or 58.

Tutorialspoint

Updated on: 10-Oct-2022

7K+ Views

Kickstart Your Career

Get certified by completing the course

Get Started