Question

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

• A. $\frac{8}{11}$
• B. $\frac{8}{11}$
• C. $\frac{7}{9}$
• D. $\frac{4}{3}$

Answer 1

The correct option is B

$\frac{8}{11}$

Let the numerator of the rational number = x

Then the denominator of the rational number = x + 3
When the numerator is increased by 7, then new numerator = x + 7
When the denominator is decreased by 1, then new denominator = x + 3 - 1
The new number formed = $\frac{3}{2}$
According to the question,
$\frac{x+7}{x+3-1}$ $=\frac{3}{2}$
$\Rightarrow \frac{x+7}{x+2}$ $=\frac{3}{2}$
$\Rightarrow$ 2(x + 7) = 3(x + 2)
$\Rightarrow$ 2x + 14 = 3x + 6
$\Rightarrow$ 3x - 2x = 14 - 6
$\Rightarrow$ x = 8
So, original number = $=\frac{8}{11}$