Question

Sum of the numerator and the denominator of a fraction is 12. If the denominator is increared by 3 then fraction becomes 1/2. Find the fraction.

Answer 1

Let the fraction be $\frac{p}{q}$

Then $p+q=12$

$\Rightarrow p=12-q$

$\frac{p}{q+3}=\frac{1}{2}$

$\Rightarrow 2(12-q)=q+3$

$\Rightarrow 24-2q=q+3$

$\Rightarrow 24-3=q+2q$

$\to 21=3q$

$q=7$

$p=12-q=5$

Fraction$=\frac{5}{7}$.