Question

The denominator of a rational number is greater than its numerator by $3$. If $3$ is subtracted from the numerator and $2$ is added to its denominator, the new number becomes $1/5$. The original number is ___________.

• A. $-\frac{5}{8}$
• B. $\frac{5}{8}$
• C. $\frac{3}{8}$
• D. $-\frac{3}{8}$

Answer 1

Answer: (B)

$\frac{5}{8}$

Let the rational number be $\frac{x}{y}$

Given denominator y is greater than numerator x by 3

$\Rightarrow y-x=3$

$y=x+3$

Let new rational number be $\frac{z}{w}$

Given $z=x-3$ and $w=y+2=x+3+2=x+5$

$\frac{x-3}{x+5}=\frac{1}{5}$

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

$5x-15=x+5$

$5x-x=15+5$

$4x=20$

$x=\frac{20}{4}=5$

$y=x+3=5+3=8$

The original number is $\frac{5}{8}$