Five men or ten women can complete a job in 20 days. Find the time in which four men and four women can complete it (in days)

Options

A. 15
B. 20
C. `13(1)/(3)`
D. `16(2)/(3)`

Explanation

To solve the problem, we will first determine the work done by men and women in terms of work units, and then find out how long it takes for 4 men and 4 women to complete the job.

### Step 1: Determine the total work done by men and women together.
Given that 5 men or 10 women can complete the job in 20 days, we can calculate the total work in terms of man-days or woman-days.

- Work done by 5 men in 20 days = 5 men * 20 days = 100 man-days.
- Work done by 10 women in 20 days = 10 women * 20 days = 200 woman-days.

Since 5 men can do the same work as 10 women in the same time, we can equate the work done:
- 100 man-days = 200 woman-days.

### Step 2: Find the work done by one man and one woman.
From the above, we can derive the work done by one man and one woman:
- 1 man = 2 women (since 5 men = 10 women).

Now, let's express the work done by one man in terms of woman-days:
- If 1 man = 2 women, then 1 man can do the work of 2 women in the same time.

### Step 3: Calculate the work done by 4 men and 4 women.
Now, we need to find out how much work 4 men and 4 women can do together in one day.

- Work done by 4 men in one day = 4 men * (1/20) of the job = 4/20 = 1/5 of the job.
- Work done by 4 women in one day = 4 women * (1/20) of the job = 4/20 = 1/5 of the job.

Now, adding the work done by men and women together:
- Total work done by 4 men and 4 women in one day = (1/5 + 1/5) = 2/5 of the job.

### Step 4: Calculate the time taken to complete the job.
To find the total time taken to complete the job, we can use the formula:
- Time = Total Work / Work done in one day.

Since the total work is 1 job:
- Time = 1 job / (2/5 job per day) = 1 * (5/2) = 5/2 days = 2.5 days.

### Final Answer:
Thus, 4 men and 4 women can complete the job in **2.5 days**.

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