Question

Denominator of rational number is 4 less than its numerator if 11 is added to numerator and 1 is subtracted from denominator the new number becomes $\frac{7}{3}$ Find the rational number

• A. $\frac{23}{27}$
• B. $\frac{27}{23}$
• C. $\frac{13}{17}$
• D. $\frac{17}{13}$

Answer 1

The correct option is D $\frac{17}{13}$

Let the rational number be $\frac{x}{y}$
Given, Denominator of rational number is 4 less than its numerator $=>y=x-4=>x-y=4$ --- (1)
Also, if $11$is added to numerator and $1$ is subtracted from denominator the new number, then number $=\frac{x+11}{y-1}=\frac{7}{3}$
$=>3x+33=7y-7$
$=>3x-7y=-40$ --- (2)

Multiplying equation $\left(1\right)$ with $3$ we get, $3x-3y=12$ ----- equation $\left(3\right)$

Subtracting equation $\left(3\right)$
from $\left(2\right)$, we get $4y=52=>y=13$

Substituting $y=13$ in the
equation $\left(1\right)$, we get $x=13=4=>x=17$
Hence, the number is $\frac{17}{13}$