To solve this problem, we first need to determine the total work done in terms of "person-days" for building huts and then find out how many people (let's denote them by \( x \)) would take 15 days to build 6 huts.
Step 1: Calculate the Work in Person-Days for the Initial Scenario
We know from the problem that 5 people can build 3 huts in 21 days.
The total work done in person-days is calculated as:
\[ \text{Total Work} = \text{Number of People} \times \text{Days} = 5 , \text{people} \times 21 , \text{days} = 105 , \text{person-days} \]
This total work is for building 3 huts. Therefore, the work required to build 1 hut is:
\[ \text{Work per Hut} = \frac{105 , \text{person-days}}{3 , \text{huts}} = 35 , \text{person-days per hut} \]
Step 2: Calculate the Work Required for 6 Huts
Now, we need to find the total work required to build 6 huts:
\[ \text{Total Work for 6 Huts} = 6 , \text{huts} \times 35 , \text{person-days per hut} = 210 , \text{person-days} \]
Step 3: Determine How Many People are Required to Build 6 Huts in 15 Days
Let \( x \) be the number of people needed. We want these \( x \) people to complete 210 person-days of work in 15 days:
\[ \text{Total Work in person-days} = x , \text{people} \times 15 , \text{days} \]
Setting this equal to the required work we found earlier:
\[ x \times 15 = 210 \]
Now, we solve for \( x \):
\[ x = \frac{210}{15} = 14 \]
Conclusion
Thus, the number of people required to build 6 huts in 15 days is 14 people.