Question

If the numerator is decreased by 1 and denominator is multiplied by 2, then the resulting fraction is $\frac{1}{5}$.If the numerator is increased by 12 and denominator is multiplied by 6, then the resulting fraction is $\frac{1}{2}$. What is the difference between the numerator and the denominator?

• A. 1
• B. -2
• C. 3
• D. -5

Answer 1

The correct option is B -2

Let the fraction be $\frac{x}{y}$. Then, according to question, we have
$\frac{x-1}{2y}=\frac{1}{5}$ and $\frac{x+12}{6y}=\frac{1}{2}$
On simplification, $5x-2y=\mathrm{5...}\left(1\right)$
$2x-6y=-24⟹x-3y=-\mathrm{12...}\left(2\right)$
From (2), $x=3y-12$.
Substituting this value of $x$ in (1), $5(3y-12)-2y=5⟹13y=65⟹y=5$
$x=3y-12=3\left(5\right)-12=3$
$⟹x-y=3-5=-2$