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1. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is :

A. 18

B. 24

C. 42

D. 81

Solution:

Let the ten's and unit's digits be

x

and

\frac{8}{x}

respectively
Then,

\begin{aligned} \Leftrightarrow (10 x + \frac{8}{x}) + 18 = 10 \times \frac{8}{x} + x \\ \Leftrightarrow 10 x^{2} + 8 + 18 x = 80 + x^{2} \\ \Leftrightarrow 9 x^{2} + 18 x - 72 = 0 \\ \Leftrightarrow x^{2} + 2 x - 8 = 0 \\ \Leftrightarrow (x + 4) (x - 2) = 0 \\ \Leftrightarrow x = 2 \end{aligned}

So, ten's digit = 2 and unit's digit = 4
Hence, required number = 24

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