The product of two fractions is 14/15 and their quotient is 35/24 . The greater fraction is :

Answer: Option B

Let the two fractions be a and b
Then,
$$\begin{array}{rl}& ab=\frac{14}{15}\&\frac{a}{b}=\frac{35}{24}\\ & \iff \frac{ab}{\left(\frac{a}{b}\right)}=\left(\frac{14}{15}\times \frac{24}{35}\right)\\ & \iff b^2=\frac{16}{25}\\ & \iff b=\frac{4}{5}\\ & \text{So, }\\ & \iff ab=\frac{14}{15}\\ & \iff a=\left(\frac{14}{15}\times \frac{5}{4}\right)\\ & \iff a=\frac{7}{6}\end{array}$$
Since a > b,
So, greater fraction is $$\frac{7}{6}$$