Question

If the difference between the reciprocal of a positive proper fraction and the fraction itself be $\frac{9}{20}$ then the fraction is

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

Answer 1

Answer: (C)

$\frac{4}{5}$

Let the fraction be $\frac{x}{y}$, then reciprocal = $\frac{y}{x}$
Given $\frac{y}{x}-\frac{x}{y}=\frac{9}{20}\Rightarrow$ $\frac{y^2-x^2}{xy}=\frac{9}{20}$
The only options where $xy=20$ are (c) and (d)
but in (d) y will be 4 and x will be 9
$\therefore$ $y^2-x^2=16-25=-9$ (negative) hence the
option satisfying the given condition is option
i.e. $\frac{x}{y}=\frac{4}{5}$