If 16 men or 20 women can do a piece of work in 25 days, in what time will 28 men and 15 women do it ?

Options

A. `14(2)/(7)` days
B. `33(1)/(3)` days
C. `18(3)/(4)` days
D. 10 days

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Determine the total work done by men and women in days.
We know that:
- 16 men can complete the work in 25 days.
- 20 women can complete the work in 25 days.

### Step 2: Calculate the total work in man-days.
The total work can be calculated in terms of man-days:
- Work done by 16 men in 25 days = 16 men × 25 days = 400 man-days.

### Step 3: Calculate the total work in woman-days.
Similarly, for women:
- Work done by 20 women in 25 days = 20 women × 25 days = 500 woman-days.

### Step 4: Find the work done by one man and one woman in one day.
Now, let's find the work done by one man in one day:
- Since 16 men complete the work in 25 days, one man will take 400 days to complete the work alone. Thus, the work done by one man in one day = 1/400 of the work.

Now, for one woman:
- Since 20 women complete the work in 25 days, one woman will take 500 days to complete the work alone. Thus, the work done by one woman in one day = 1/500 of the work.

### Step 5: Calculate the work done by 28 men in one day.
Now we calculate the work done by 28 men in one day:
- Work done by 28 men in one day = 28 × (1/400) = 28/400 = 7/100 of the work.

### Step 6: Calculate the work done by 15 women in one day.
Now we calculate the work done by 15 women in one day:
- Work done by 15 women in one day = 15 × (1/500) = 15/500 = 3/100 of the work.

### Step 7: Combine the work done by men and women.
Now, we add the work done by 28 men and 15 women in one day:
- Total work done in one day = (7/100) + (3/100) = (7 + 3)/100 = 10/100 = 1/10 of the work.

### Step 8: Calculate the total time taken to complete the work.
If 28 men and 15 women together can complete 1/10 of the work in one day, then to complete the entire work:
- Time taken = 1 / (1/10) = 10 days.

### Final Answer:
Thus, 28 men and 15 women will complete the work in **10 days**.

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