Question

A fraction becomes $2$ when $1$ is added to both the numerator and the denominator. It becomes $3$ when $1$ is subtracted from both the numerator and the denominator. The numerator of the given fraction is

• A. $7$
• B. $4$
• C. $3$
• D. $2$

Answer 1

Answer: (A)

$7$

Let the numerator of the fraction be $x$ and the denominator be $y$.

Then by the first condition,

$\frac{x+1}{y+1}=2$
$\Rightarrow x+1=2y+2$
$\Rightarrow x=2y+1$ ..........(i)

And by the second condition,

$\Rightarrow$$\frac{x-1}{y-1}=3$

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

Comparing (i) & (ii), we get

$\Rightarrow$$2y+1=3y-2$

$\Rightarrow y=3$

So, $x=3y-2$ $=3\times 3-2=7$

$\therefore x=7$