Question

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?

Answer 1

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

According to the question,

$a-b=3$ or $b-a=3$ ...... (1)

And $10a+b+10b+a=143\Rightarrow 11a+11b=143$

$\Rightarrow a+b=13$ ...... (2)

By adding equations (i) and (ii) , we get

$2a=16or2b=16\Rightarrow a=8orb=8$

Putting value of $a\text{or}b$ in (i), we get

$b=5$ or $a=5$

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