Question

The difference of the digits of a two-digit number is $3$. If the digits are interchanged, and the resulting number is added to the original number, then we get $143$. What is the original number?

Answer 1

Let the digits of the number be $a$ and $b$ such that the number is either $(10a+b)$ or $(10b+a)$.

Given:

$a-b=3$ …… (1)

$b-a=3$ …… (2)

If the number is $(10a+b)$, then according to the question,

$10a+b+10b+a=143$

$a+b=13$ …… (3)

From equations (1) and (2), we get

$a=8$ and $b=5$

From equations (2) and (3), we get

$a=5$ and $b=8$

Hence, the required number is $85$ or $58$.