A fraction is such that if the double of the numerator and the triple pf the denominator is changed by +10 percent and -30 percent respectively, then we get 11 percent of $$\frac{16}{21}$$. Find the fraction :

Let the fraction be $$\frac{x}{y}$$
Then,
$$\eqalign{ & \Leftrightarrow \frac{{110\% {\text{ of 2}}x}}{{70\% {\text{ of 3}}y}} = 11\% {\text{ of }}\frac{{16}}{{21}} \cr & \Leftrightarrow \frac{{22x}}{{21y}} = \frac{{11}}{{100}} \times \frac{{16}}{{21}} \cr & \Leftrightarrow \frac{x}{y} = \left( {\frac{{11}}{{100}} \times \frac{{16}}{{21}} \times \frac{{21}}{{22}}} \right) \cr & \Leftrightarrow \frac{x}{y} = \frac{2}{{25}} \cr} $$