Question

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

• A. $18$
• B. $24$
• C. $42$
• D. $81$

Answer 1

The correct option is B $24$

Let the units digit be $x$.
Hence, ten's digit is $\frac{8}{x}$

Hence, the number is $10.\frac{8}{x}+x$

Now acc. to condition

$\frac{80}{x}+x+18=10x+\frac{8}{x}$

$80+x^2+18x=10x^2+8$
$9x^2-18x-72=0$
$x^2-2x-8=0$
$x^2-4x+2x-8=0$
$x(x-4)+2(x-4)=0$
$(x+2)(x-4)=0$
$x=-2$ and $x=4$
Hence, the ten's digit is $\frac{8}{4}=2$

Hence, the number is $24$