Question

If the numerator of a fraction is decreased by 2 and its denominator is decreased by 4, the value of the fraction remains the same. Find the fraction.

• A. $\frac{2}{5}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B $\frac{1}{2}$

Let us assume the numerator to be $x$ and the denominator to be $y$. This gives us the fraction as $\frac{x}{y}$.
Now, according to the given condition.

$\frac{x-2}{y-4}=\frac{x}{y}$
multiplying both the sides with $(y-4)\left(y\right)$

$(x-2)\left(y\right)=\left(x\right)(y-4)$
$xy-2y=xy-4x$
$-2y=-4x$
$⟹\frac{x}{y}=\frac{1}{2}=0.5$