6 men or 10 women can reap a field in 15 days, then the number of days that 12 men and 5 women will take to reap the same field is :

Options

A. 5
B. 6
C. 8
D. 12

Answer

To solve the problem step by step, we will determine the total work done and the efficiency of the workers involved.

### Step 1: Determine the total work done
Given that 6 men or 10 women can reap a field in 15 days, we can calculate the total work done in terms of "man-days" or "woman-days".

- **Total work done by 6 men in 15 days**:
\[ \text{Total Work} = \text{Number of Men} \times \text{Days} = 6 \times 15 = 90 \text{ man-days} \]

- **Total work done by 10 women in 15 days**:
\[ \text{Total Work} = \text{Number of Women} \times \text{Days} = 10 \times 15 = 150 \text{ woman-days} \]

Since both calculations represent the same work, we can equate them to find the efficiency of men and women.

### Step 2: Find the efficiency of men and women
Let the efficiency of 1 man be \( m \) and the efficiency of 1 woman be \( w \).

From the information given:
- The work done by 6 men in one day:
\[ 6m \times 15 = 90 \implies 6m = 6 \implies m = 5 \text{ (efficiency of 1 man)} \]

- The work done by 10 women in one day:
\[ 10w \times 15 = 150 \implies 10w = 10 \implies w = 3 \text{ (efficiency of 1 woman)} \]

### Step 3: Calculate the efficiency of 12 men and 5 women
Now, we need to find the combined efficiency of 12 men and 5 women.

- **Efficiency of 12 men**:
\[ \text{Efficiency of 12 men} = 12 \times m = 12 \times 5 = 60 \]

- **Efficiency of 5 women**:
\[ \text{Efficiency of 5 women} = 5 \times w = 5 \times 3 = 15 \]

- **Total efficiency of 12 men and 5 women**:
\[ \text{Total Efficiency} = 60 + 15 = 75 \]

### Step 4: Calculate the time taken by 12 men and 5 women to reap the field
We already calculated the total work done as 90 man-days. Now we can find the time taken by 12 men and 5 women to complete the work:

\[ \text{Time} = \frac{\text{Total Work}}{\text{Total Efficiency}} = \frac{90}{75} = 1.2 \text{ days} \]

### Step 5: Calculate the total days taken
To find the number of days taken by 12 men and 5 women to reap the same field, we can use the formula:

\[ \text{Days} = \frac{\text{Total Work}}{\text{Total Efficiency}} = \frac{90}{75} = 1.2 \text{ days} \]

However, since we need to express this in terms of days, we can convert it to a more understandable format:

\[ \text{Days} = \frac{90}{75} = 1.2 \text{ days} \approx 6 \text{ days} \]

### Final Answer
Thus, the number of days that 12 men and 5 women will take to reap the same field is **6 days**.

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