1. Problem 116: Find when all three stoves need refilling simultaneously. We use the Least Common Multiple (LCM) of the refill times 18, 24, and 30 minutes. 2. Calculate prime factorizations: - 18 = $2 \times 3^2$ - 24 = $2^3 \times 3$ - 30 = $2 \times 3 \times 5$ 3. LCM takes the highest powers of each prime: - For 2: $2^3$ - For 3: $3^2$ - For 5: $5$ 4. Calculate LCM: $$LCM = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360$$ Answer: 360 minutes (option a). --- 5. Problem 117: Number of complete combo packs with 2 samosas, 3 jalebis, and 4 idlis. Given quantities: 180 samosas, 150 jalebis, 120 idlis. 6. Calculate how many packs each ingredient can make: - Samosas: $\frac{180}{2} = 90$ - Jalebis: $\frac{150}{3} = 50$ - Idlis: $\frac{120}{4} = 30$ 7. The maximum number of complete packs is the minimum of these: 30. Answer: 30 packs (option a). --- 8. Problem 118: When will all three restock together? Restock days: 12, 15, 20. 9. Find LCM of 12, 15, and 20. Prime factorizations: - 12 = $2^2 \times 3$ - 15 = $3 \times 5$ - 20 = $2^2 \times 5$ 10. LCM takes highest powers: - 2: $2^2$ - 3: $3$ - 5: $5$ 11. Calculate LCM: $$LCM = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$$ Answer: 60 days (option b). --- 12. Problem 119: Ravi doubles samosas to 360, Meera has 150 jalebis, Arjun has 120 idlis. 13. Calculate max identical boxes: - Samosas: $\frac{360}{2} = 180$ - Jalebis: $\frac{150}{3} = 50$ - Idlis: $\frac{120}{4} = 30$ 14. Minimum is 30, so max boxes = 30. Answer: 30 (option a). --- 15. Problem 120: Each combo pack has 3 samosas and 3 jalebis. Available: 180 samosas, 150 jalebis. 16. Calculate max packs: - Samosas: $\frac{180}{3} = 60$ - Jalebis: $\frac{150}{3} = 50$ 17. Minimum is 50, so max packs = 50. Answer: 50 (option c).