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 ). 

( 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.