Question

The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, then the new number becomes $\frac{3}{2}$. Find the original number.

• A. $\frac{8}{11}$
• B. $\frac{5}{8}$
• C. $\frac{7}{10}$
• D. $\frac{2}{5}$

Answer 1

The correct option is A

$\frac{8}{11}$

Let the numerator of a rational number be $x$.
Then the denominator of a rational number would be $(x+3)$.

When the numerator is increased by $7$, it becomes $(x+7)$
When the denominator is decreased by 1, it becomes
$\Rightarrow x+3-1=x+2$

The new number formed $=\frac{3}{2}$

$\text{So,}\frac{(x+7)}{(x+2)}=\frac{3}{2}2x+14=3x+63x-2x=14-6x=8$

$\therefore$ Numerator, $x=8$
Denominator, $x+3=8+3=11$

Hence, the original rational number is $\frac{8}{11}$