If the numerator of a fraction is increased by 60% and the denominator is increased by 40%, then resultant fraction is $$\frac{{16}}{{63}}.$$ The original fraction is:

$$\eqalign{ & {\text{Let numerator}} = 5x \cr & {\text{denominator}} = 5y \cr & {\text{So as per question}} \cr & \frac{{5x + 3x}}{{5y + 2y}} = \frac{{16}}{{23}} \to \frac{x}{y} = \frac{2}{9} \cr & {\text{So the original fraction}}\,\frac{{5x}}{{5y}} = \frac{2}{9} \cr} $$