Question

A fraction is equivalent to $\frac{3}{5}$ and when $2$ is added to both the numerator and the denominator, the result is equivalent to $\frac{5}{8}$. Identify the original fraction.

• A. $\frac{8}{14}$
• B. $\frac{3}{6}$
• C. $\frac{13}{22}$
• D. $\frac{18}{30}$

Answer 1

The correct option is D $\frac{18}{30}$

Let $x$ is numerator and $y$ is denominator

Then $\frac{x}{y}=\frac{3}{5}$

$\Rightarrow 5x=3y$

$\Rightarrow 5x-3y=0$........(1)

$\Rightarrow \frac{x+2}{y+2}=\frac{5}{8}$

$\Rightarrow 8x+16=5y+10$

$\Rightarrow 8x-5y=-6$........(2)

Multiply (1) by $5$, we get

$25x-15y=0$........(3)

Multiply (2) by $3$ we get

$24x-15y=-18$......(4)

Subtract equation (3) whit (4), we get

$\Rightarrow x=18$

Put $x=18$ in (1), we get

$5\times 18-3y=0$

$\Rightarrow 3y=90$

$\Rightarrow y=30$

Then fraction is $\frac{x}{y}=\frac{18}{30}$