If 4 men or 6 women can do a piece of work in 12 days workIng 7 hours a day, how many days will it take to complete a work twice as large with 10 men and 3 women working together 8 hours a day?

Options

A. 6 days
B. 7 days
C. 8 days
D. 10 days

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total work done in man-hours.
Given that 4 men can complete the work in 12 days working 7 hours a day, we first calculate the total work in terms of man-hours.

Total work = Number of men × Number of days × Number of hours per day
Total work = 4 men × 12 days × 7 hours/day = 336 man-hours

### Step 2: Determine the work done by 1 man in 1 hour.
To find out how much work 1 man can do in 1 hour, we divide the total work by the total number of man-hours.

Total man-hours = 4 men × 12 days × 7 hours/day = 336 man-hours
Work done by 1 man in 1 hour = Total work / Total man-hours
Work done by 1 man in 1 hour = 1 / 336

### Step 3: Calculate the work done by 10 men and 3 women in 1 hour.
We need to express the work done by women in terms of men. We know from the problem that:
4 men = 6 women
Thus, 1 man = 1.5 women

Now, we can express 3 women in terms of men:
3 women = 3/1.5 = 2 men

So, 10 men + 3 women = 10 men + 2 men = 12 men.

Now, we calculate the work done by 12 men in 1 hour:
Work done by 12 men in 1 hour = 12 × (1 / 336) = 12 / 336 = 1 / 28

### Step 4: Calculate the total work needed for the larger job.
The problem states that the new job is twice as large as the original job. Therefore, the total work required for the larger job is:
Total work for larger job = 2 × Total work = 2 × 336 = 672 man-hours

### Step 5: Calculate the number of hours required to complete the larger job.
Now, we need to find out how many hours it will take for 12 men to complete 672 man-hours of work.

Using the work done in 1 hour:
Total hours required = Total work / Work done by 12 men in 1 hour
Total hours required = 672 / (1 / 28) = 672 × 28 = 18816 hours

### Step 6: Convert hours into days.
Since the men are working 8 hours a day, we convert the total hours into days:
Total days required = Total hours required / Hours per day
Total days required = 18816 / 8 = 2352 days

### Final Answer:
It will take 2352 days to complete the work twice as large with 10 men and 3 women working together 8 hours a day.

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