Question

the sum of the digits of a two-digit number is 12 if the number formed by reversing the digits is greater than the original number by 54 find the original number

Answer 1

Let the two digit number be 10x + y
Given that sum of the digits = 12
Therefore x + y = 12 (Equation 1)

Also given that the numbers formed by reversing the digits is 54 greater than the original number.
Therefore
10y + x = 10x + y + 54
10x + y - 10y - x = - 54
9x - 9y = - 54
Taking 9 as common
x - y = - 6 (Equation 2)

Adding equation 1 and 2
x + y = 12
x - y = - 6

2x = 6
x = 3

3 + y= 12
y = 9

The number is 10x+ y =10(3) + 9 = 39

Hope this helps you.