Two numbers are in the ratio 17 : 45. One-third of the smaller is less than 1/5 of the bigger by 15. The… · ABC26GN3101

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