Question

The denominator of a rational number is 4 more than the numerator. If 2 is added to the numerator and 3 is added to denominator then the new number becomes $\frac{3}{4}$. Find the original number

• A. $\frac{11}{15}$
• B. $\frac{12}{16}$
• C. $\frac{13}{17}$
• D. $\frac{10}{14}$

Answer 1

Answer: (C)

$\frac{13}{17}$

Let the numerator of the rational number be $x$.
Then, the denominator of the rational number $=x+4$
It is given that the numerator is increased by 2 and the denominator is increased by 3 to get the new rational number $\frac{3}{4}$.
According to the given condition,
$\frac{x+2}{(x+4)+3}=\frac{3}{4}$

By cross multiplying, we get

$4(x+2)=3(x+7)⟹4x+8=3x+21⟹4x-3x=21-8$ ....[Transposing $3x$ to LHS and $8$ to RHS]

or $x=13$
Therefore, numerator of the rational number $=13$ and denominator $=13+4=17$.
Hence the original rational number is $\frac{13}{17}$.