Question

The numerator of a fraction is one more than its denominator. If its reciprocal is subtracted from it, the difference is $\frac{11}{30}$. Find the fraction.

• A. $\frac{7}{6}$
• B. $\frac{6}{5}$
• C. $-\frac{6}{5}$
• D. None of these

Answer 1

The correct option is B $\frac{6}{5}$

Let the denominator be $x$.
Hence the fraction will be $\frac{x+1}{x}$
Applying the given condition, we get
$\frac{x+1}{x}-\frac{x}{x+1}=\frac{11}{30}$

$30\left(\right(x+1{)}^2-x^2)=11(x(x+1))$
$30(2x+1)=11x^2+11x$
$60x+30=11x^2+11x$
$11x^2-49x-30=0$

Solving this quadratic equation, we get

$x=\frac{49\pm \sqrt{{49}^2-4\left(11\right)(-30)}}{22}$

$\therefore x=5,\frac{-6}{11}$

Taking the negative value we get
$\frac{\frac{-6}{11}+1}{\frac{-6}{11}}=\frac{5}{-6}$
Substituting the positive value we get
$\frac{5+1}{5}$$=\frac{6}{5}$