Question

the sum of the of two digits number is 12. The number obtained interchanging the digit exceeds the original number by 54.Find the original no.

Answer 1

Given sum of the digits is 12
Let the digits in ones place be x
Hence the digit in tens place is (12 – x)
The original number = 10(12 – x) + x = 120 – 9x
Number formed by reversing the digits = 10x + (12 – x)  =  9x + 12
Given that number formed by reversing the digits is 54 greater than the original number.
⇒ 9x + 12 = (120 – 9x) + 54 = 174 – 9x
⇒ 18x = 174 – 12 = 162
∴ x = 9
The original number = 120 – 9x = 120 – 9(9) = 39

Answer 2

let the two digits of the number be x and y( where y is at one's place and x is at ten's place)

so x +y = 12

\the two digit number will be
10*x+y

so as per ques, on interchaning the digits
10y + x = 10x + y + 54
=> 10y -y = 10x - x + 54
=> 9y-9x = 54

taking 9 as common 
x-y = 6                  -------1
and x +y = 12       -------2
so on solving these 2 equations  
y = 9 and x = 3

so original number is 
10*3 + 9 = 39