Question

The denominater of a fraction is greater than its numerator by 12. If the numerator is decreases by 2 and the denominator is increased by 7,the new fraction is equivalent with $\frac{1}{2}$. Find the fraction

Answer 1

Let x be the numerator and y be the denominator of the fraction.

It is given, $y=x+12$ …………$\left(1\right)$

and $\frac{x-2}{y+7}=\frac{1}{2}$

$\Rightarrow 2(x-2)=y+7$

$\Rightarrow 2x-4=y+7$

$\Rightarrow 2x-4=x+12+7$

$\Rightarrow 2x-4=x+19$

$\Rightarrow x=19+4$

$\Rightarrow x=23$

From $\left(1\right)$, $y=23+12$

$=35$

Hence the required fraction, $\frac{x}{y}=\frac{23}{35}$.