Question

The product of two fractions is $\frac{14}{15}$ and their quotient is $\frac{35}{24}$. The greater fraction is:

• A. $\frac{4}{5}$
• B. $\frac{7}{6}$
• C. $\frac{7}{4}$
• D. $\frac{7}{3}$

Answer 1

The correct option is B

$\frac{7}{6}$

Let fraction = $\frac{a}{b},\frac{c}{d}$

$\therefore$ $\frac{ac}{bd}=\frac{14}{15},\frac{ad}{bc}=\frac{35}{24}$

Now, $\left(\frac{ac}{bd}\right)\left(\frac{ad}{bc}\right)=\left(\frac{14}{15}\right)\left(\frac{35}{24}\right)=\frac{49}{36}$

$\Rightarrow \frac{a}{b}=\frac{7}{6}\therefore \frac{c}{d}=\frac{4}{5}$

$\therefore$ Greater fraction = $\frac{7}{6}$