1. **Problem Statement:** Find the number of chairs that can be purchased for 56500 if 17 chairs cost 9605. 2. **Formula:** Use direct proportion formula: $$\frac{\text{Cost}_1}{\text{Quantity}_1} = \frac{\text{Cost}_2}{\text{Quantity}_2}$$ 3. **Calculation:** Let the number of chairs be $x$. $$\frac{9605}{17} = \frac{56500}{x}$$ Cross-multiply: $$9605x = 17 \times 56500$$ $$9605x = 960500$$ Divide both sides by 9605: $$x = \frac{960500}{9605} = 100$$ 4. **Answer:** 100 chairs can be purchased for 56500. --- 1. **Problem Statement:** 10 boys can dig a pitch in 12 hours. Find how long 8 boys will take. 2. **Formula:** Inverse proportion: $$\text{Time}_1 \times \text{Workers}_1 = \text{Time}_2 \times \text{Workers}_2$$ 3. **Calculation:** Let time taken by 8 boys be $t$. $$12 \times 10 = t \times 8$$ $$120 = 8t$$ $$t = \frac{120}{8} = 15$$ 4. **Answer:** 8 boys will take 15 hours. --- 1. **Problem Statement:** A man works 8 hours daily and finishes work in 12 days. Find days if he works 6 hours daily. 2. **Formula:** Total work = hours per day $\times$ days. Work is constant. 3. **Calculation:** Total work = $8 \times 12 = 96$ hours. Let days needed be $d$: $$6 \times d = 96$$ $$d = \frac{96}{6} = 16$$ 4. **Answer:** He will finish in 16 days. --- 1. **Problem Statement:** 15 masons build a wall in 20 days. Find masons needed to build in 12 days. 2. **Formula:** Work is constant, so: $$\text{Masons}_1 \times \text{Days}_1 = \text{Masons}_2 \times \text{Days}_2$$ 3. **Calculation:** Let masons needed be $m$. $$15 \times 20 = m \times 12$$ $$300 = 12m$$ $$m = \frac{300}{12} = 25$$ 4. **Answer:** 25 masons are needed. --- 1. **Problem Statement:** 20 persons complete a job in 42 days. Find days for 56 persons. 2. **Formula:** $$\text{Persons}_1 \times \text{Days}_1 = \text{Persons}_2 \times \text{Days}_2$$ 3. **Calculation:** Let days be $d$. $$20 \times 42 = 56 \times d$$ $$840 = 56d$$ $$d = \frac{840}{56} = 15$$ 4. **Answer:** 56 persons will complete in 15 days. --- 1. **Problem Statement:** Provisions for 400 persons last 23 days. If 60 more join, find days provisions last. 2. **Formula:** Total provision = persons $\times$ days (constant). 3. **Calculation:** Total provision = $400 \times 23 = 9200$ person-days. Let days be $d$: $$(400 + 60) \times d = 9200$$ $$460d = 9200$$ $$d = \frac{9200}{460} = 20$$ 4. **Answer:** Provisions last 20 days. --- 1. **Problem Statement:** 6 pipes fill a tank in 64 minutes. Find pipes needed to fill in 96 minutes. 2. **Formula:** Work rate is inversely proportional to time: $$\text{Pipes}_1 \times \text{Time}_1 = \text{Pipes}_2 \times \text{Time}_2$$ 3. **Calculation:** Let pipes needed be $p$. $$6 \times 64 = p \times 96$$ $$384 = 96p$$ $$p = \frac{384}{96} = 4$$ 4. **Answer:** 4 pipes are needed. --- 1. **Problem Statement:** 17 men complete work in 42 hours. Find men needed to complete in 34 hours. 2. **Formula:** $$\text{Men}_1 \times \text{Hours}_1 = \text{Men}_2 \times \text{Hours}_2$$ 3. **Calculation:** Let men needed be $m$. $$17 \times 42 = m \times 34$$ $$714 = 34m$$ $$m = \frac{714}{34} = 21$$ 4. **Answer:** 21 men are needed. --- 1. **Problem Statement:** 500 soldiers have food for 30 days. 125 soldiers leave. Find days food lasts. 2. **Formula:** Total food = soldiers $\times$ days. 3. **Calculation:** Total food = $500 \times 30 = 15000$ soldier-days. Let days be $d$: $$(500 - 125) \times d = 15000$$ $$375d = 15000$$ $$d = \frac{15000}{375} = 40$$ 4. **Answer:** Food lasts 40 days. --- 1. **Problem Statement:** 5 pumps empty tank in 36 minutes. Find time for 9 pumps. 2. **Formula:** $$\text{Pumps}_1 \times \text{Time}_1 = \text{Pumps}_2 \times \text{Time}_2$$ 3. **Calculation:** Let time be $t$. $$5 \times 36 = 9 \times t$$ $$180 = 9t$$ $$t = \frac{180}{9} = 20$$ 4. **Answer:** 9 pumps take 20 minutes. --- 1. **Problem Statement:** Andy reads 21 pages daily, finishes in 30 days. Find days if reading 18 pages daily. 2. **Formula:** Total pages = pages/day $\times$ days. 3. **Calculation:** Total pages = $21 \times 30 = 630$ pages. Let days be $d$: $$18 \times d = 630$$ $$d = \frac{630}{18} = 35$$ 4. **Answer:** Andy will finish in 35 days. --- 1. **Problem Statement:** 15 laborers build wall in 28 days. Find how many more needed to finish in 21 days. 2. **Formula:** $$\text{Laborers}_1 \times \text{Days}_1 = \text{Laborers}_2 \times \text{Days}_2$$ 3. **Calculation:** Let laborers needed be $x$. $$15 \times 28 = x \times 21$$ $$420 = 21x$$ $$x = \frac{420}{21} = 20$$ More laborers needed = $20 - 15 = 5$. 4. **Answer:** 5 more laborers are needed. --- 1. **Problem Statement:** 18 men finish work in 42 days. Find how many more men to finish in 36 days. 2. **Formula:** $$\text{Men}_1 \times \text{Days}_1 = \text{Men}_2 \times \text{Days}_2$$ 3. **Calculation:** Let men needed be $m$. $$18 \times 42 = m \times 36$$ $$756 = 36m$$ $$m = \frac{756}{36} = 21$$ More men needed = $21 - 18 = 3$. 4. **Answer:** 3 more men are needed. --- **Final note:** All problems use direct or inverse proportion and unitary method to find unknown quantities by setting up proportional relationships and solving for the unknown.