Question

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
• E. None of these

Answer 1

The correct option is B

24

Let the ten's and units digit be x and $\frac{8}{x}$ respectively.

Then, $\begin{array}{c}\left(10x+\frac{8}{x}\right)+18=10\times \frac{8}{x}+x\iff 10x^2+8+18x=80+x^2\\ \iff 9x^2+18x-72=0\iff x^2+2x-8=0\iff (x+4)(x-2)=0\iff x=2\end{array}$

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