Question

The sum of the digits of a 2-digit number is 6. The number obtained by interchanging its digits is 18 more than the original number. Find the original number.

Answer 1

Let the two numbers of the two-digit number be 'a' and 'b'.

$a+b=6$ ... (1)

The number can be written as $(10a+b)$.
After interchanging the digits, the number becomes $(10b+a)$.

$$\begin{gathered} (10a+b)+18=(10b+a) \\ 9a-9b=-18 \end{gathered}$$
$a-b=-2$ ... (2)

Adding equations (1) and (2):
$2a=4\Rightarrow a=2$

Using $a=2$ in equation (1):
$b=6-a=6-2=4$

Therefore, the original number is 24.