Question

Five people can build 3 hatsin 21 days find the number of apple working at the same rate would build similar 6 huts in 15 days

Answer 1

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**.