Question

If $2$ is added to numerator and deducted from the denominator it becomes equal to $1$. On the other hand if $3$ is added to denominator and $3$ is added to numerator it becomes equal to $1/3$, the number is____.

• A. $4/9$
• B. $7/10$
• C. $8/12$
• D. $9/15$

Answer 1

The correct option is C $8/12$

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

As per question,

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

Also

$\frac{x-3}{y+3}=\frac{1}{3}\to 3x-9=y+3\to 3x-y-12=0-\left(2\right)$

Solving eqs.(1) and (2)

we get $x=8,y=12$

Hence the fraction be $\frac{8}{12}$