Question

The number obtained by interchanging the digits of a two digit number is less than the original number by 54. If the sum of the digits of the number is 12, what is the original number?
A) 29
B) 93
C) 74
D) Cannot be determined
E) None of these

Answer 1

Let the tens place of the number be x

Let the ones place of the number be y

So the number is 10x+y

The number obtained by reversing the digit is 10y+x

Now

10y+x=10x+y-54

9y-9x=54

y-x=6.....(1)

Again

x+y=12.....(2)

Now adding equation (1) and (2) we get

y-x+x+y=6+12

2y=18

y=9

Putting the value of y in (1) we get

9-x=6

x=3

So the number is 10*3+9=39

So the correct option is(E)None of these

Hope this helped.....