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When $1$ is subtracted from the numerator and $2$ is added to the denominator of a fraction, it becomes $\frac{1}{2}$. When $7$ is subtracted from the numerator and $2$ is subtracted from the denominator, the fraction becomes $\frac{1}{3}$. Find the fraction.
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(b) Let numerator be $x$ and denominator be $y$
$\therefore$ fraction is $\frac{x}{y}$
$\frac{x-1}{y+2} = \frac{1}{2} \Rightarrow 2x - y = 4$ ............(i) (1 Mark)
and $\frac{x-7}{y-2} = \frac{1}{3} \Rightarrow 3x - y = 19$ ............(ii) (1 Mark)
Solving (i) and (ii), we get $x = 15, y = 26$ (1 Mark)
$\Rightarrow$ fraction is $\frac{15}{26}$
(b) Let numerator be $x$ and denominator be $y$
$\therefore$ fraction is $\frac{x}{y}$
$\frac{x-1}{y+2} = \frac{1}{2} \Rightarrow 2x - y = 4$ ............(i) (1 Mark)
and $\frac{x-7}{y-2} = \frac{1}{3} \Rightarrow 3x - y = 19$ ............(ii) (1 Mark)
Solving (i) and (ii), we get $x = 15, y = 26$ (1 Mark)
$\Rightarrow$ fraction is $\frac{15}{26}$