Question

If the numerator of a fraction is increased by 2 and its denominator is decreased by 1, it becomes $\frac{2}{3}$. If the numerator is increased by 1 and the denominator is increased by 2, it becomes $\frac{1}{3}$. Find the fraction.

• A. $x=2andy=7$
• B. $x=-2andy=-7$
• C. $x=3andy=7$
• D. $x=2andy=6$

Answer 1

The correct option is A

$x=2andy=7$

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

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

$\Rightarrow 3x-2y=-8....\left(i\right)$
$and3x-y=-\mathrm{1......}\left(ii\right)$

$\Rightarrow 3x-2y=-8$
$-(3x-y=-1)$

$\Rightarrow 3x-2y=-8$
$-3x+y=1$
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$-y=-7$
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$\Rightarrow y=7$

Substituting y = 7 in equation (ii), we get
$3x-\left(14\right)=-8$
$3x=-8+14=6$
$\therefore x=2$

$\Rightarrow x=2andy=7$