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1. The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers ?

A. 29

B. 70

C. 92

D. Cannot be determined

Solution:

Let the ten's digit be x and unit's digit be y
Then,

\begin{aligned} \Leftrightarrow (10 x + y) - (10 y + x) = 63 \\ \Leftrightarrow 9 (x - y) = 63 \\ \Leftrightarrow x - y = 7 \end{aligned}

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