The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54. If the sum of the two digit of the number is 12, then what is the original number ?

Let ten's digit = x
Then, unit's digit = (12 - x)
$$\therefore \left[ {10x + \left( {12 - x} \right)} \right] - $$    $$\left[ {10\left( {12 - x} \right) + x} \right]$$   $$ = 54$$
$$\eqalign{ & \Leftrightarrow 18x - 108 = 54 \cr & \Leftrightarrow 18x = 162 \cr & \Leftrightarrow x = 9 \cr} $$
So, ten's digit = 9 and unit's digit = 3
Hence, original number = 93