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 ?

Answer: Option E

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