Question

The sum of the numerator and the denominator of a fraction is equal to $12$. Three times the numerator is one more than double the denominator. If the fraction is $\frac{p}{q}$, then

• A. $p=q+2$
• B. $p+2=q$
• C. $pq=30$
• D. $\frac{p}{q}=2$

Answer 1

The correct option is B $p+2=q$

$p+q=12$ ........... (1)
$3p=2q+1$ ............... (2)
Multiplying equation (1) by 3, we get
$3p+3q=36$ .......... (3)
Substituting the value of 3p from equation (2) in equation (3), we get
$2q+1+3q=36$
or $5q=35$ or $q=7$
$\therefore p=5$
Hence, $p+2=q$