Question

A positive number when decreased by $4$ becomes $21$ times its reciprocal. The number is

• A. $8$
• B. $7$
• C. $6$
• D. $5$

Answer 1

The correct option is B $7$

Let the positive number be $x$.
Hence,
$x-4=\frac{21}{x}$
Hence
$x^2-4x=21$
$x^2-4x-21=0$
$x^2-7x+3x-21=0$
$x(x-7)+3(x-7)=0$
$(x+3)(x-7)=0$
$x=-3$ and $x=7$
Since then number is positive, the number is $7$.