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.

Question

Philoid · Accepted Answer

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 ).
( 10a + b ) + 18 = ( 10b + a ) 9a − 9b = −18
a − b = −2 ... (2)
Adding equations (1) and (2):
2a = 4

∴ a = 2
Using a = 2 in equation (1),
b = 6 – a = 6 – 2 = 4
Therefore, the original number is 24.