If 3 men or 4 women can reap a field in 43 days, how long will 7 men and 5 women take to reap it?

Options

A. 7 days
B. 11 days
C. 12 days
D. 16 days

Answer

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

### Step 1: Determine the total work done
Given that 3 men or 4 women can reap a field in 43 days, we first need to find the total work done in terms of man-days or woman-days.

- **Total work done by 3 men in 43 days:**
\[ \text{Work} = \text{Number of men} \times \text{Days} = 3 \text{ men} \times 43 \text{ days} = 129 \text{ man-days} \]

- **Total work done by 4 women in 43 days:**
\[ \text{Work} = \text{Number of women} \times \text{Days} = 4 \text{ women} \times 43 \text{ days} = 172 \text{ woman-days} \]

### Step 2: Find the efficiency of men and women
To find the efficiency of men and women, we will assume that the work done is equal, thus we can find the efficiency of one man and one woman.

- **Efficiency of 3 men:**
\[ \text{Efficiency of 3 men} = \frac{129 \text{ man-days}}{43 \text{ days}} = 3 \text{ men} \Rightarrow \text{Efficiency of 1 man} = \frac{129}{3 \times 43} = 1 \text{ unit/day} \]

- **Efficiency of 4 women:**
\[ \text{Efficiency of 4 women} = \frac{172 \text{ woman-days}}{43 \text{ days}} = 4 \text{ women} \Rightarrow \text{Efficiency of 1 woman} = \frac{172}{4 \times 43} = 1 \text{ unit/day} \]

### Step 3: Calculate the total efficiency of 7 men and 5 women
Now we will calculate the total efficiency of 7 men and 5 women.

- **Total efficiency of 7 men:**
\[ \text{Efficiency of 7 men} = 7 \times 1 = 7 \text{ units/day} \]

- **Total efficiency of 5 women:**
\[ \text{Efficiency of 5 women} = 5 \times 1 = 5 \text{ units/day} \]

- **Combined efficiency:**
\[ \text{Total efficiency} = 7 + 5 = 12 \text{ units/day} \]

### Step 4: Calculate the total work in units
From Step 1, we found that the total work is 129 man-days or 172 woman-days. We can use either of these to find the total work in units.

- **Total work (in units):**
\[ \text{Total work} = 129 \text{ units} \]

### Step 5: Calculate the time taken by 7 men and 5 women to complete the work
Now we can find out how many days it will take for 7 men and 5 women to complete the work.

- **Time taken (in days):**
\[ \text{Time} = \frac{\text{Total work}}{\text{Total efficiency}} = \frac{129 \text{ units}}{12 \text{ units/day}} = 10.75 \text{ days} \]

### Final Answer
Thus, it will take approximately **10.75 days** for 7 men and 5 women to reap the field.

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