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

$$\eqalign{ & {\text{A}}:{\text{B}} \cr & 17:45 \cr & 17x:45x \cr & {\text{Given}} \cr & \Rightarrow 17x \times \frac{1}{3} + 15 = 45x \times \frac{1}{5} \cr & \Rightarrow \frac{{17x + 45}}{3} = 9x \cr & \Rightarrow 17x + 45 = 27x \cr & \Rightarrow 10x = 45 \cr & \Rightarrow x = \frac{{45}}{{10}} \cr & \therefore {\text{Smaller number is }} \cr & = \frac{{45}}{{10}} \times 17 \cr & = \frac{{765}}{{10}} \cr & = 76\frac{1}{2} \cr} $$