Question

The denominator of a fraction is $1$ more than twice its numerator. If $1$ is added to numerator and denominator respectively, the ratio of numerator to denominator is $1:2$.Find the fraction.

Answer 1

According to given $y=2x+1\Rightarrow 2x-y+1=\mathrm{0....}\left(i\right)$

According to second given line condition

$\frac{x+1}{y+1}=\frac{1}{2}$

$2(x+1)=y+1\Rightarrow 2x+2=y+1$

$2x-y=1-2$

$2x-y=-\mathrm{1.....}\left(ii\right)$

There can be infinite values of satisfying the conditions some possibles are

$x=3,y=7\Rightarrow$ $\left(i\right)$ $2\left(3\right)-7+11=0\Rightarrow 6-7+1=0\Rightarrow 0=0$

$\left(ii\right)$ $2\left(3\right)-2=-1\Rightarrow 6-7=-1\Rightarrow -1=-1$

$x=4,y=9\Rightarrow$ $\left(i\right)$ $2\left(3\right)-9+1=0\Rightarrow 8-9+1=0\Rightarrow 0=0$

$\left(ii\right)$ $2\left(4\right)-8=-1\Rightarrow 8-9=1\Rightarrow -1=-1$

Therefore the fraction can be }$