Question

A two digit number is such that the product of its digits is 28. When 112 is subtracted from the number, the digits interchange their places. Find the second degree equation in x from which we can find tens digit.

• A. $9x^2-112x-252=0$
• B. $7x^2-112x-252=0$
• C. $9x^2-102x-252=0$
• D. $9x^2-112x-242=0$

Answer 1

The correct option is A

$9x^2-112x-252=0$

Let the tens digit be x. Then, the units digit $=\frac{28}{x}$

$\therefore$ Number $=10x+\frac{28}{x}$

Number obtained by interchanging the digits $=10\times \frac{28}{x}+x$

$\therefore (10x+\frac{28}{x})-(10\times \frac{28}{x}+x)$
$=112$

$\Rightarrow 10x+\frac{28}{x}-\frac{280}{x}-x=112$

$\Rightarrow 9x-\frac{252}{x}-112=0$

$\Rightarrow 9x^2-112x-252=0$