12 women can do a piece of work in 20 days. If the 4 women deny to work, then how many more days are required?

Options

A. 6
B. 10
C. 15
D. none of these

Answer

To solve the problem step by step, we will use the concept of work done by a group of people.

### Step 1: Understand the initial conditions
We know that 12 women can complete a piece of work in 20 days.

### Step 2: Calculate the total work in terms of woman-days
Total work can be calculated as:
\[ \text{Total Work} = \text{Number of Women} \times \text{Number of Days} = 12 \text{ women} \times 20 \text{ days} = 240 \text{ woman-days} \]

### Step 3: Determine the number of women available after 4 women deny to work
If 4 women deny to work, the number of women left is:
\[ 12 - 4 = 8 \text{ women} \]

### Step 4: Set up the equation for the new scenario
Let \( D_2 \) be the number of days required for 8 women to complete the same work. Using the formula for work:
\[ \text{Total Work} = \text{Number of Women} \times \text{Number of Days} \]
we can write:
\[ 240 \text{ woman-days} = 8 \text{ women} \times D_2 \]

### Step 5: Solve for \( D_2 \)
Rearranging the equation gives:
\[ D_2 = \frac{240 \text{ woman-days}}{8 \text{ women}} = 30 \text{ days} \]

### Step 6: Calculate the additional days required
Now, we need to find out how many more days are required compared to the original 20 days:
\[ \text{Additional Days} = D_2 - D_1 = 30 \text{ days} - 20 \text{ days} = 10 \text{ days} \]

### Final Answer
Thus, the number of additional days required is **10 days**.

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