Question

The numerator of a rational number is $4$ less than its denominator. If $1$ is added to the numerator and denominator both, the rational number becomes $\frac{1}{8}$. Find the number.

• A. $\frac{3}{25}$
• B. $\frac{25}{7}$
• C. $\frac{-3}{25}$
• D. None of the above.

Answer 1

Answer: (C)

$\frac{-3}{25}$

Let the denominator of the rational no. be $x$.

Then, numerator $\left(n\right)=x-4$

Add $1$ to both numerator and denominator,
Denominator = $x+1$ and Numerator =$x-4+1=x-3$

$⟹\frac{x-3}{x+1}=\frac{1}{8}$

$⟹8x-24=x+1$

$⟹7x=25$

$x=\frac{25}{7}$

Numerator $=\frac{25}{7}-4=\frac{25-28}{7}=\frac{-3}{7}$
Rational number = $\frac{-3}{7}\times \frac{7}{25}=\frac{-3}{25}$