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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 ?

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 ? Correct Answer None of these

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

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