Question

The sum of the digits of a two digit number is 12. If the new number formed by interchanging the digits is greater than original number by 18 find the original number.

Answer 1

Answer:

We can check it by doing the sum, we get 9 + 3 = 12. And also by reversing the number we get 93. So, the difference between 93 and 39 is 54. So, the number 39 is the right number.

Answer 2

Answer:

Let A and B The digit

$a + b \: = 12...(1)$

$54 + (10a + b) = (10b + a)$

$54 + 10a + b = 10b + a$

$9a - 9b = - 54$

$a - b = - 6...(2)$

Adding (1) and (2)

a +b =12

a - b = -6

_______

2a = 6

a = 3

so b = 9

39 + 54 = 93 (verified)

orig number = 39 and number when digits reversed = 93