1. **State the problem:** We are given that 8 men can dig a field in 9 days. We need to find: a) How long will it take for 18 men to dig the same field? b) How many men can dig the same field in 3 days? 2. **Understand the work concept:** The total amount of work (digging the field) is constant. The work done is proportional to the number of men times the number of days. 3. **Calculate total work in man-days:** Since 8 men take 9 days, total work = $8 \times 9 = 72$ man-days. 4. **Find time taken by 18 men:** Let the time taken be $t$ days. Total work = number of men $\times$ time $$72 = 18 \times t$$ Solve for $t$: $$t = \frac{72}{18} = 4$$ So, 18 men can dig the field in 4 days. 5. **Find number of men to dig in 3 days:** Let the number of men be $m$. Using the total work, $$72 = m \times 3$$ Solve for $m$: $$m = \frac{72}{3} = 24$$ So, 24 men can dig the same field in 3 days. **Final Answers:** - Time for 18 men: 4 days - Number of men for 3 days: 24 men