Question

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

HI there !

Let the no: in unit place be "y" and in ten's place be "x"
The original no: would be 10x + y

Given :-

x + y = 12              ----> (1)

When the digits are interchanged , the no: would be 10y+x

A.T.Q ,

10x + y + 54 = 10y + x

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

9x - 9y = -54

9(x - y) = -54

x - y = -6                ---> (2)

Adding equations (1) and (2) , we get :-

x + y = 12
x - y = -6
========
2x  = 6

x = 3

x + y = 12

3 + y = 12

y = 9

====================================

The original no: is :-

10x + y 

10 × 3 + 9
= 39

The original no: is 39