Question

the sum of the digits of a two number is 12. the f 54 is subtracted from the number, the digits get reversed. find the number

Answer 1

Let the digits of the number are x and y, so number will be (10x+y)
A/q,
x+y =12
and, (10x +y) -54 = (10y +x)
⇒9x -9y = 54
⇒x-y =6
⇒x =(6 +y), putting this value in first equation,
(6 +y) +y =12
⇒2y =6
⇒y =3
so, x= 6+3 =9
so, the number will be 93

Answer 2

Let the digits of the number be x and y
the number = 10x+y
Given x+y = 12   --------------------(1)
Also given 10x+y -54 = 10y+x  
⇒10x + y - 10y - x = 54 
⇒9x - 9y - 54 = 0 
⇒9( x - y - 6 = 0)
⇒x - y -6 = 0/9
⇒ x - y = 6  --------------------(2)
Adding (1) from (2)
   x + y = 12
   x -  y = 6

⇒2x - 0 = 18
⇒ x = 18/2 
∴x = 9
Substituting x = 9 in (1)
⇒ x+y =12
⇒9+y = 12
⇒y = 12-9
∴ y = 3
Therefore the number is 10x + y  
                                    = 10(9) + 3  
                                    = 90 + 3
                                    = 93
∴The number is 93