1. **Stating the problem:** We need to divide 240 into two parts in a given ratio and find the smaller share. 2. **Understanding the ratio:** Suppose the ratio is $a:b$. The total parts are $a+b$. 3. **Formula for each share:** - First share = $\frac{a}{a+b} \times 240$ - Second share = $\frac{b}{a+b} \times 240$ 4. **Finding the smaller share:** The smaller share corresponds to the smaller part in the ratio. 5. **Example:** If the ratio is not given, let's assume a ratio $x:y$. Without the ratio, we cannot find the exact smaller share. Please provide the ratio to calculate the smaller share.