Question

The difference between a positive proper function and its reciprocal is $9/20$. The fraction is:

• A. $\frac{3}{5}$
• B. $\frac{3}{10}$
• C. $\frac{4}{5}$
• D. $\frac{4}{3}$

Answer 1

Answer: (C)

$\frac{4}{5}$

Let the required fraction be $x$. Then $\frac{1}{x}.x=\frac{9}{20}$
$\therefore$ $\frac{1-x^2}{x}=\frac{9}{20}$
$\Rightarrow$ $20-20x^2=9x$
$\Rightarrow$ $20x^2+9x-20=0$
$\Rightarrow$ $20x^2+25x-16x-20=0$
$\Rightarrow$ $5x(4x+5)-4(4x+5)=0$
$\Rightarrow$ $(4x+5)(5x-4)=0$
$x=\frac{4}{5}$