Five people can build 3 huts in 21 days.find the number of people working at the same rate that will built 6 similar hut in 15 days?

Let's first calculate the total work required to build 3 huts in 21 days.

Total work = 3 huts

Let's assume each hut is equivalent to 1 unit of work.

So, total work = 3 units

Now, let's calculate the work done by 5 people in 21 days:

Work done by 5 people in 21 days = 5 * 21 = 105 people-days

Now, let's find the work done by 1 person in 1 day:

Work done by 1 person in 1 day = Total work / Total days
Work done by 1 person in 1 day = 3 / 105 = 1/35 units

Now, let's find the number of people required to build 6 huts in 15 days:

Total work = 6 huts

Total work = 6 units

Work done by 1 person in 1 day = 1/35 units

Let the number of people required be x.

Work done by x people in 15 days = x * 15 * (1/35) = 6

Solving for x:

x * 15 * (1/35) = 6
x * 15 = 6 * 35
x = (6 * 35) / 15
x = 14

Therefore, 14 people working at the same rate can build 6 similar huts in 15 days.

Given:

- 5 people build 3 huts in 21 days
- Number of huts built = 3
- Number of days taken = 21
- Number of people = 5

To find:

- Number of people required to build 6 huts in 15 days

Step 1: Find the work done by 5 people in 1 day.

Work done = Number of huts built - Number of days taken
Work done = 3 - 21 = 63 units

Step 2: Calculate the work required to build 6 huts in 15 days.

Work required = Number of new huts - Number of new days
Work required = 6 - 15 = 90 units

Step 3: Calculate the number of people required to do the work.

Number of people = Work required / Work done by 5 people in 1 day
Number of people = 90 / 63 = 10 people

Therefore, 10 people working at the same rate will build 6 similar huts in 15 days.