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.
Solution:
Let the two numbers of the two-digit number be 'a' and 'b'.
$a+b=6$ ....(1)
The number can be written as $(10 a+b)$.
After interchanging the digits, the number becomes $(10 b+a)$.
$(10 a+b)+18=(10 b+a)$
$9 a-9 b=-18$
$a-b=-2$ ..(2)
Adding equations (1) and (2):
$2 a=4 \Rightarrow a=2$
Using $a=2$ in equation (1):
$b=6-a=6-2=4$
Therefore, the original number is 24 .