Question

The denominator of a rational number is greater than its numerator by $5$. If the numerator is increased by $6$ and denominator is decreased by $3$, the number becomes $\frac{5}{3}$. Find the original number.

• A. $\frac{9}{4}$
• B. $\frac{4}{9}$
• C. $\frac{-4}{9}$
• D. None of the above.

Answer 1

Answer: (B)

$\frac{4}{9}$

Let the numerator of the rational number $=p$
Then, the denominator of the rational number $=p+5$
When numerator is increased by $6$, the new numerator $=p+6$
When denominator decreased by $3$, the new denominator $=p+2$

According to the question, $\frac{p+6}{p+2}=\frac{5}{3}$

$⟹3p+18=5p+10$
$⟹2p=8$

$\therefore p=4$
Numerator $=p=4$
Denominator$=p+5=4+5=9$

Original number = $\frac{4}{9}$