Question

A fraction becomes $\frac{1}{3}$ when $1$ is subtracted from the numerator and it becomes $\frac{1}{4}$ when $8$ is added to its denominator. Find the fraction.

• A. $\frac{1}{4}$
• B. $\frac{4}{17}$
• C. $\frac{5}{12}$
• D. None of these

Answer 1

Answer: (C)

$\frac{5}{12}$

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

Now as per the question we will have

$\frac{x-1}{y}=\frac{1}{3}..\left(1\right)$

$\frac{x}{y+8}=\frac{1}{4}..\left(2\right)$

From eq1 will get

$3x-y=\mathrm{3...}\left(3\right)$

From eq2 will get

$4x-y=\mathrm{8...}\left(4\right)$

Now subtract eq4 from eq3

$\Rightarrow 3x-y-4x+y=3-8$

$\Rightarrow -x=-5$

$\Rightarrow x=5$

Now put x in eq 4 will get

$\Rightarrow 4\times 5-y=8$

$\Rightarrow 20-y=8$

$\Rightarrow -y=8-20$

$\Rightarrow -y=-12$

$\Rightarrow y=12$

Hence fraction will be $\frac{5}{12}$