1. **Problem 7:** Sana cleaned $\frac{1}{4}$ of her house, and her sister cleaned $\frac{1}{5}$ of the remaining part. Find the ratio of clean to unclean parts. 2. **Step 1:** Calculate the remaining part after Sana cleaned: $$1 - \frac{1}{4} = \frac{3}{4}$$ 3. **Step 2:** Calculate the part cleaned by Sana's sister: $$\frac{1}{5} \times \frac{3}{4} = \frac{3}{20}$$ 4. **Step 3:** Total cleaned part: $$\frac{1}{4} + \frac{3}{20} = \frac{5}{20} + \frac{3}{20} = \frac{8}{20} = \frac{2}{5}$$ 5. **Step 4:** Unclean part: $$1 - \frac{2}{5} = \frac{3}{5}$$ 6. **Step 5:** Ratio of clean to unclean: $$\frac{2}{5} : \frac{3}{5} = 2 : 3$$ --- 7. **Problem 8:** Two sums of money are in the ratio 5 : 8. The smaller amount is 65. Find the larger amount. 8. **Step 1:** Let the smaller amount be $5x$ and the larger amount be $8x$. 9. **Step 2:** Given $5x = 65$, solve for $x$: $$x = \frac{65}{5} = 13$$ 10. **Step 3:** Find the larger amount: $$8x = 8 \times 13 = 104$$ --- 11. **Problem 9:** The weight of 15 feet of wire is 6 pounds. How many pounds will 25 feet of the same wire weigh? 12. **Step 1:** Find weight per foot: $$\frac{6}{15} = 0.4 \text{ pounds per foot}$$ 13. **Step 2:** Weight of 25 feet: $$25 \times 0.4 = 10 \text{ pounds}$$ --- 14. **Problem 10:** If 6 boys can dig a ditch in 8 hours, how many hours would it take 10 boys working at the same rate? 15. **Step 1:** Total work = number of boys $\times$ time = $$6 \times 8 = 48 \text{ boy-hours}$$ 16. **Step 2:** Time taken by 10 boys: $$\frac{48}{10} = 4.8 \text{ hours}$$ --- **Final answers:** 7. Ratio of clean to unclean = $2 : 3$ 8. Larger amount = 104 9. Weight of 25 feet wire = 10 pounds 10. Time taken by 10 boys = 4.8 hours