Question

The sum of the numerator and the denominator of a fraction is equal to $7$. Four times the numerator is $8$ less than $5$ times the denominator. Find the fraction.

• A. $\frac{1}{6}$
• B. $\frac{3}{4}$
• C. $\frac{4}{7}$
• D. $\frac{7}{11}$

Answer 1

The correct option is B $\frac{3}{4}$

Let the fraction be $\frac{x}{y}$

Given, the sum of the numerator and the denominator of a fraction is equal to $7$

$\Rightarrow x+y=7$ $...\left(1\right)$
Also, four times the numerator is $8$ less than $5$ times the denominator

$\Rightarrow 4x=5y-8$

or $4x-5y=-8$ $...\left(2\right)$

Multiplying equation $\left(1\right)$ with $5$

We get $5x+5y=35$ $...\left(3\right)$

Adding equations $\left(2\right)$ and $\left(3\right),$

$4x-5y=-8$

$5x+5y=35$
______________
$9x=27$

$\Rightarrow 9x=27$

$\Rightarrow x=3$

Substituting $x=3$ in the equation $\left(1\right)$
We get $3+y=7$

$\Rightarrow y=4$

Hence, the fraction is $\frac{3}{4}$