Question

The sum of a 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

there are two methods of solving this question the first one is sort method and the other one is longitude I will be telling you the short method in this answer
now according to the question the sum of the digits of the number is 12 so X + Y = 12 Now since x and y are digit of the number both are less than or equal to 9 and also sum of these is 12
number satisfying above condition are
(3,9), (4,8) , (5 ,7) , (6,6) now will check each of these for the second condition that is when they are reversed the difference is 54 we will see that only( 3,9 ) will satisfy as 93 - 39 equal to 54

Answer 2

let two digit number be x and y
number: 10x+y

according to question
x+y=12••••••eq (1)
& 10x + y+ 54= 10y+x•••••eq(2)
10y-y +x -10x= 54
9y - 9x = 54
or y-x =6
y =6+x••••• eq 3
putting value of y in eq 1

x +(6+x) = 12
2x + 6= 12
or x+ 3= 6
x =3
now in eq 3
y= 6+3
y = 9

therefore , number will be 39