A particular work can be completed by 6 men and 6 women in 24 days, whereas the same work can be completed by 8 men and 12 women in 15 days. Find :
According to the amount of work done, one man is equivalent to how many women.

Answer

To solve the problem step by step, we need to analyze the information provided and set up equations based on the work done by men and women.

### Step 1: Calculate the total work done by 6 men and 6 women in 24 days.

The total work can be represented as:
\[ \text{Total Work} = \text{Number of Workers} \times \text{Days} \]
For 6 men and 6 women working together for 24 days:
\[ \text{Total Work} = (6 + 6) \times 24 = 12 \times 24 = 288 \text{ man-days} \]

### Step 2: Calculate the work done by 8 men and 12 women in 15 days.

Similarly, for 8 men and 12 women working together for 15 days:
\[ \text{Total Work} = (8 + 12) \times 15 = 20 \times 15 = 300 \text{ man-days} \]

### Step 3: Set up the equations for work done.

From the two scenarios, we can equate the total work done:
\[ 288 \text{ man-days} = 300 \text{ man-days} \]

### Step 4: Express the work done in terms of men and women.

Let the work done by one man in one day be \( m \) and by one woman be \( w \). Then we can express the work done in terms of \( m \) and \( w \):
1. From the first scenario:
\[ 6m + 6w = \frac{288}{24} = 12 \quad \text{(work done in one day)} \]
Simplifying gives:
\[ m + w = 2 \quad \text{(Equation 1)} \]

2. From the second scenario:
\[ 8m + 12w = \frac{300}{15} = 20 \quad \text{(work done in one day)} \]
Simplifying gives:
\[ 2m + 3w = 5 \quad \text{(Equation 2)} \]

### Step 5: Solve the equations simultaneously.

We can solve Equation 1 and Equation 2 together. From Equation 1:
\[ w = 2 - m \]
Substituting \( w \) in Equation 2:
\[ 2m + 3(2 - m) = 5 \]
Expanding and simplifying:
\[ 2m + 6 - 3m = 5 \]
\[ -m + 6 = 5 \]
\[ -m = -1 \implies m = 1 \]
Now substituting \( m = 1 \) back into Equation 1:
\[ 1 + w = 2 \implies w = 1 \]

### Step 6: Find the equivalent of one man in terms of women.

From our calculations:
- One man can do the work equivalent to one woman.

Thus, the final answer is:
\[ \text{One man is equivalent to } 1 \text{ woman.} \]