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 the denominator, the new number becomes $\frac{1}{5}$. Then the original fraction was _________.

• A. $\frac{7}{11}$
• B. $\frac{3}{5}$
• C. $\frac{5}{8}$
• D. $\frac{4}{7}$

Answer 1

Answer: (C)

$\frac{5}{8}$

Let, the numerator of rational fraction be $x$

$\therefore$ the denomiantor $=x+3$

A.T.Q,

$\frac{x-3}{x+3+2}=\frac{1}{5}$

$⟹\frac{x-3}{x+5}=\frac{1}{5}$

$⟹5x-15=x+5$

$⟹5x-x=5+15$

$⟹4x=20$

$⟹x=\frac{20}{4}=5$

$\therefore$ The original rational fraction is $\frac{5}{5+3}=\frac{5}{8}$