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1. 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 ?

A. 28

B. 39

C. 82

D. Cannot be determined

Solution:

Let ten's digit = x
Then, unit's digit = (12 - x)

∴ [10 x + (12 - x)] -

[10 (12 - x) + x]

= 54

\begin{aligned} \Leftrightarrow 18 x - 108 = 54 \\ \Leftrightarrow 18 x = 162 \\ \Leftrightarrow x = 9 \end{aligned}

So, ten's digit = 9 and unit's digit = 3
Hence, original number = 93

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