Question

The numerator of a fraction is $5$ less than its denominator. If $3$ is added to the numerator and denominator both, the fraction becomes $\frac{4}{5}$. Find the original fraction.

• A. $\frac{1}{22}$
• B. $\frac{17}{22}$
• C. $\frac{17}{2}$
• D. $\frac{7}{22}$

Answer 1

The correct option is B $\frac{17}{22}$

Let the denominator be $x$

Fraction$=\frac{x-5}{x}$

$\frac{x-5+3}{x+3}=\frac{4}{5}$

$\frac{x-2}{x+3}=\frac{4}{5}$

$5(x-2)=4(x+3)$

$5x-4x=12+10$

$x=22$

So, numerator$=x-5=22-5=17$

and denominator$=22$

So, the original fraction$=\frac{17}{22}$