Question

A fraction becomes $4$ when $1$ is added to both the numerator and denominator and it becomes $7$ when 1 is subtracted from both. The numerator of the given fraction is?

• A. $12$
• B. $13$
• C. $15$
• D. $17$

Answer 1

The correct option is C $15$

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

It is given that fraction becomes $4$ when $1$ is added to both the numerator and denominator and it becomes $7$ when $1$ is subtracted from both, therefore,

$\frac{x+1}{y+1}=4x+1=4y+4x-4y=3........\left(1\right)\frac{x-1}{y-1}=7x-1=7y-7x-7y=-6........\left(2\right)$

Now subtract equation 1 from equation 2:

$x-7y-x+4y=-6-3$

$-3y=-9$

$y=3$

Substitute the value of $y$ in equation 1:

$x-4\left(3\right)=3$

$x-12=3$

$x=3+12=15$

Therefore, the fraction is $\frac{15}{3}$ and hence the numerator of the fraction is $15$.