Question

A fraction become $\frac{1}{2}$ if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more then its numerator, Find the fraction.

• A. $-\frac{12}{17}$
• B. $\frac{12}{37}$
• C. $\frac{1}{17}$
• D. $\frac{12}{17}$

Answer 1

The correct option is D $\frac{12}{17}$

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

According to question,

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

$\Rightarrow 2(x-5)=y-3$

$\Rightarrow 2x-10=y-3$

$\Rightarrow 2x-y=\mathrm{7...}\left(1\right)$

and $y=5+x$

$\Rightarrow -x+y=\mathrm{5...}\left(2\right)$

Adding equation 1 and 2 we get,

$2x-y-x+y=7+5\Rightarrow x=12$

Putting value of x in equation 2 we have,

$-12+y=5\Rightarrow y=5+12=17$

Thus, the fraction becomes, $\frac{12}{17}$