Question

Frame and solve the equations for the following statements:
The denominator of a fraction is $2$ more than its numerator. If one is added to both the numerator and their denominator the fraction becomes $\frac{2}{3}$. Find the fraction

Answer 1

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

Therefore Numerator is $x$ and Denominator is $y$

according to the question $y=x+2$

Now, adding $1$ to $x$ and $y$

$\Rightarrow \frac{x+1}{y+1}=\frac{2}{3}$

Now, Putting $y=x+2$

$\Rightarrow \frac{x+1}{x+2+1}=\frac{2}{3}\Rightarrow 3x+3=2x+6\Rightarrow x=3$

Since, $y=x+2\Rightarrow y=5$

Hence, the numbers are $3$ and $5$.