Question

If the same number is added to both the numerator and denominator of a fraction $\frac{3}{5}$, then the result is $\frac{3}{4}$. Find the number.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

Let the number be $x$.
According to the given condition, we have
$\frac{3+x}{5+x}=\frac{3}{4}$

$\Rightarrow 4(3+x)=3(5+x)$ ....[By cross-multiplication]

$\Rightarrow 12+4x=15+3x$

$\Rightarrow 4x-3x=15-12$ ....[Transposing $3x$ to LHS and $12$ to RHS]

$\Rightarrow x=3$