1. Problem 12: The cost of 17 chairs is 9605. Find the number of chairs that can be purchased for 56500. Using the unitary method: Cost of 1 chair = $\frac{9605}{17}$ Number of chairs for 56500 = $\frac{56500}{\frac{9605}{17}}$ = $\frac{56500 \times 17}{9605}$ = 100 chairs 2. Problem 13: 10 boys can dig a pitch in 12 hours. Find how long 8 boys will take. Work done by 10 boys in 12 hours = 1 pitch Work done by 1 boy in 1 hour = $\frac{1}{10 \times 12}$ Work done by 8 boys in 1 hour = $8 \times \frac{1}{120} = \frac{8}{120} = \frac{1}{15}$ Time taken by 8 boys = $\frac{1}{\frac{1}{15}} = 15$ hours 3. Problem 14: A man works 8 hours daily and finishes work in 12 days. Find days if he works 6 hours daily. Total work = $8 \times 12 = 96$ hours Days if working 6 hours daily = $\frac{96}{6} = 16$ days 4. Problem 15: 15 masons build a wall in 20 days. Find masons needed to build in 12 days. Work = $15 \times 20 = 300$ mason-days Masons needed = $\frac{300}{12} = 25$ masons 5. Problem 16: 9 persons complete a job in 42 days. Find days for 56 persons. Work = $9 \times 42 = 378$ person-days Days for 56 persons = $\frac{378}{56} = 6.75$ days 6. Problem 17: Provisions for 400 persons last 23 days. If 60 more join, find days provisions last. Total person-days = $400 \times 23 = 9200$ New persons = $400 + 60 = 460$ Days = $\frac{9200}{460} = 20$ days 7. Problem 18: 6 pipes fill a tank in 64 minutes. Find pipes needed to fill in 96 minutes. Work = $6 \times 64 = 384$ pipe-minutes Pipes needed = $\frac{384}{96} = 4$ pipes 8. Problem 19: 17 men complete work in 42 hours. Find men needed to complete in 34 hours. Work = $17 \times 42 = 714$ man-hours Men needed = $\frac{714}{34} = 21$ men 9. Problem 20: 500 soldiers have food for 30 days. 125 soldiers transferred. Find days food lasts. Total soldier-days = $500 \times 30 = 15000$ Remaining soldiers = $500 - 125 = 375$ Days = $\frac{15000}{375} = 40$ days 10. Problem 21: 5 pumps empty tank in 36 minutes. Find time with 9 pumps. Work = $5 \times 36 = 180$ pump-minutes Time with 9 pumps = $\frac{180}{9} = 20$ minutes 11. Problem 22: Andy reads 21 pages daily, finishes in 30 days. Find days if reading 18 pages daily. Total pages = $21 \times 30 = 630$ Days at 18 pages/day = $\frac{630}{18} = 35$ days 12. Problem 23: 15 laborers build wall in 28 days. Find how many more needed to finish in 21 days. Work = $15 \times 28 = 420$ labor-days Laborers needed = $\frac{420}{21} = 20$ More laborers = $20 - 15 = 5$ 13. Problem 24: 18 men finish work in 42 days. Find how many more men to finish in 36 days. Work = $18 \times 42 = 756$ man-days Men needed = $\frac{756}{36} = 21$ More men = $21 - 18 = 3$