If the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is $$\frac{15}{26}$$. What was the original fraction ?

Let the fraction be $$\frac{x}{y}$$
Then,
$$\eqalign{ & \Leftrightarrow \frac{{x + 200\% {\text{ of }}x}}{{y + 300\% {\text{ of }}y}} = \frac{{15}}{{26}} \cr & \Leftrightarrow \frac{{3x}}{{4y}} = \frac{{15}}{{26}} \cr & \Leftrightarrow \frac{x}{y} = \frac{{15}}{{26}} \times \frac{4}{3} \cr & \Leftrightarrow \frac{x}{y} = \frac{{10}}{{13}} \cr} $$