1. **Problem statement:** 18 boys or 3 girls can complete a piece of work in 4 days. We need to find how many days 1 boy and 2 girls together will take to complete the same work. 2. **Step 1: Calculate total work in terms of boy-days or girl-days.** - Since 18 boys complete the work in 4 days, total work = $18 \times 4 = 72$ boy-days. - Since 3 girls complete the work in 4 days, total work = $3 \times 4 = 12$ girl-days. 3. **Step 2: Find the work rate of one boy and one girl.** - Work rate of 1 boy = $\frac{1}{72}$ work per day (because 18 boys do 1 work in 4 days, so 1 boy does $\frac{1}{72}$ work per day). - Work rate of 1 girl = $\frac{1}{12}$ work per day. 4. **Step 3: Calculate combined work rate of 1 boy and 2 girls.** - Combined rate = $\frac{1}{72} + 2 \times \frac{1}{12} = \frac{1}{72} + \frac{2}{12} = \frac{1}{72} + \frac{1}{6}$. - Find common denominator 72: $\frac{1}{72} + \frac{12}{72} = \frac{13}{72}$ work per day. 5. **Step 4: Calculate the number of days to complete the work.** - Days = $\frac{1}{\text{combined rate}} = \frac{1}{\frac{13}{72}} = \frac{72}{13} \approx 5.54$ days. **Final answer:** 1 boy and 2 girls together will complete the work in approximately $5.54$ days.