If 3 men or 9 boys can finish a work in 21 days, then in how many days can 5 men and 6 boys finish the same work?

Question

Accepted Answer

1. **Work Equivalence**:  
   - From the given data, **3 men = 9 boys**, so **1 man = 3 boys**.

2. **Total Work Calculation**:  
   - The total work done by **9 boys in 21 days** is:  
     $$
     	ext{Total Work} = 9 	imes 21 = 189 \, 	ext{boy-days}.
     $$

3. **Combined Workforce Efficiency**:  
   - The efficiency of **5 men** (in terms of boys) is:  
     $$
     5 \, 	ext{men} = 5 	imes 3 = 15 \, 	ext{boys}.
     $$  
   - Adding the efficiency of **6 boys**, the total workforce is:  
     $$
     	ext{Total Workforce} = 15 + 6 = 21 \, 	ext{boys}.
     $$

4. **Time Taken to Complete Work**:  
   - With a workforce of **21 boys**, the time required to complete **189 boy-days** of work is:  
     $$
     	ext{Time} = \frac{	ext{Total Work}}{	ext{Workforce}} = \frac{189}{21} = 9 \, 	ext{days}.
     $$

Thus, the correct answer is **B. 9 days**.

Answer

Answer

Answer