Question

If the numerator of a certain fraction is increased by 2 and the denominator increased by 1, then the resulting fraction equals $\frac{1}{2}.$ If however the numerator is increased by 1 and the denominator decreased by 2, then the resulting fraction equal $\frac{3}{5}$ Find the fraction.

• A. $\frac{2}{7}$
• B. $\frac{6}{7}$
• C. $\frac{1}{7}$
• D. $\frac{3}{7}$

Answer 1

Answer: (A)

$\frac{2}{7}$

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

Then, by the second condition,

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

$\Rightarrow y=2x+3$ ....... $\left(i\right)$

By the second condition,

$\frac{x+1}{y-2}=\frac{3}{5}$

$\Rightarrow 5x-3y=-11$

$\Rightarrow 5x-3\times (2x+3)=-11$ ........ From $\left(i\right)$

$\Rightarrow 5x-6x=-11+9$

$\Rightarrow x=2$

Putting $x=2$ in $\left(i\right)$, we get

$y=2\times 2+3=7$

$\therefore \frac{x}{y}=\frac{2}{7}$