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

Solution(By Examveda Team)

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