Two numbers are in the ratio 17 : 45. One third of the smaller is less than $$\frac{{\text{1}}}{{\text{5}}}$$ of the bigger by 15. The smaller number is -

Let the numbers be 17x and 45x
Then,
$$\eqalign{ & = \frac{1}{5}{\text{of }}45x - \frac{1}{3}{\text{of }}17x = 15 \cr & \Leftrightarrow 9x - \frac{{17}}{3}x = 15 \cr & \Leftrightarrow \frac{{10x}}{3} = 15 \cr & \Leftrightarrow x = 15 \times \frac{3}{{10}} = \frac{9}{2} \cr & \therefore {\text{Smaller number}} \cr & = 17x = \left( {17x \times \frac{9}{2}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{153}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{76}}\frac{1}{2} \cr} $$