Question

The sum of two digits of a number is 12.if 54 is subtracted from it it's digits are reversed.find the number

Answer 1

let the digits of the no be x and y
x+y=12⇒y=12-x.....(i)
ATQ
10x+y-54=10y+x
10x+12-x-54=10(12-x)+x...............(using (i) )
⇒9x-42=120-9x
⇒18x=162
⇒x=9
So the digits are 9 and 3 
And the no is 93

Answer 2

LET THE NUMBERS BE X and Y
X+Y=12

X=12-Y----------------------1
A.T.Q.
10x+y-54=10y+x
10X-X+Y-10Y=54
⇒9X-9Y=54

9(12-Y)-9Y=54

108-9Y-9Y=54

-18Y=54-108

-18Y=-54

Y=-54/-18

Y=3

PUTTING THE VALUE OF Y IN 1
X=12-3

X=9

HENCE THE NUMBER IS 93