Question

The sum of the digit of two digit number is 12.if the new number formed by reversing the digits is greater than the original number by 54.find the original number.

Answer 1

Let the units digit be x and the tens digiti be y
Then x+y = 12 or y = 12-x
The original number has (12-x) in tens digit and x in units digit
So original number = 10(12-x)+x = 120-10x+x= 120 -9x
When number is reversed we have x in tens digit and 12-x in units digit.
So reversed number = 10x+12-x= 12+9x
We are given that reversed number is greater than original number by 54
This means: 12+9x = (120-9x) +54 = 174-9x
9x+9x= 174-12
18x = 162
x = 9
so the original number is x in units digit and 12-x in tens digit which is (12-9) 9
or 39.
Answer: 39