Question

the sum of the digits of a two digit number is 12. the number formed by interchanging the digits is greater than the original number by 54.find the original number.

Answer 1

let the unit digit be x,
and the tens digit b y,

Then the number is 10y + x ,

x + y = 12

and, by interchanging the digit ,

10x + y = 10y + x + 54
9x - 9y - 54 = 0
x - y = 6

2x = 18
x = 9


x + y = 12
y = 3

So the number is 10y + x
= 39