If 3 men and 4 women can build a wall in 43 days , in how many days can 7 men and 5 women build this wall ?

Options

A. 16 days
B. 25 days
C. 21 days
D. 12 days

Answer

To solve the problem step by step, we will first determine the work done by men and women, and then calculate how long it will take for 7 men and 5 women to build the wall.

### Step 1: Determine the total work done in terms of man-days
Given that 3 men and 4 women can build a wall in 43 days, we can express the total work in terms of man-days.

Let the work done by 1 man in 1 day be \( M \) and the work done by 1 woman in 1 day be \( W \).

The total work done by 3 men and 4 women in 43 days is:
\[ \text{Total Work} = (3M + 4W) \times 43 \]

### Step 2: Express the work done by men and women
We need to express the work done by men in terms of women. We can assume that the work done by 1 man is equivalent to the work done by \( \frac{4}{3} \) women (from the information given in the question).

Thus, we can express the work done by 3 men in terms of women:
\[ 3M = 3 \times \frac{4}{3}W = 4W \]

Now substituting this back into the total work equation:
\[ \text{Total Work} = (4W + 4W) \times 43 = 8W \times 43 = 344W \]

### Step 3: Calculate the work done by 7 men and 5 women
Now we want to find out how many days it will take for 7 men and 5 women to complete the same work.

Using the same conversion, the work done by 7 men in terms of women is:
\[ 7M = 7 \times \frac{4}{3}W = \frac{28}{3}W \]

Now, the total work done by 7 men and 5 women in one day is:
\[ \text{Work done in one day} = \frac{28}{3}W + 5W = \frac{28}{3}W + \frac{15}{3}W = \frac{43}{3}W \]

### Step 4: Calculate the number of days required
Now, we know the total work is \( 344W \) and the work done in one day by 7 men and 5 women is \( \frac{43}{3}W \).

Let \( D \) be the number of days required for 7 men and 5 women to complete the work:
\[ \text{Total Work} = \text{Work done in one day} \times D \]
\[ 344W = \left(\frac{43}{3}W\right) \times D \]

Now, we can cancel \( W \) from both sides (assuming \( W \neq 0 \)):
\[ 344 = \frac{43}{3}D \]

### Step 5: Solve for \( D \)
To solve for \( D \), multiply both sides by 3:
\[ 1032 = 43D \]
Now, divide both sides by 43:
\[ D = \frac{1032}{43} = 24 \]

Thus, it will take 7 men and 5 women **24 days** to build the wall.

### Final Answer:
**24 days**