25 men and 15 women can complete a piece of work in 12 days. All of them start working together and after working for 8 days, the women stopped working 25 men completed the remaining work in 6 days. How many days will it take for completing the entire job, if only 15 women are put on the job?

Options

A. 48 days
B. 24 days
C. 36 days
D. 60 days

Answer

To solve the problem step by step, we will follow the logical sequence of calculations based on the information provided.

### Step 1: Determine the total work done by 25 men and 15 women in 12 days.

Let the efficiency of one man be \( M \) and the efficiency of one woman be \( W \).

The total work done by 25 men and 15 women in 12 days can be expressed as:
\[ \text{Total Work} = (25M + 15W) \times 12 \]

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

In the first 8 days, all 25 men and 15 women worked together:
\[ \text{Work done in 8 days} = (25M + 15W) \times 8 \]

### Step 3: Determine the remaining work after 8 days.

After 8 days, the remaining work is:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work done in 8 days} \]

### Step 4: Calculate the work done by 25 men in the next 6 days.

After the first 8 days, only the 25 men continue to work for 6 more days:
\[ \text{Work done by 25 men in 6 days} = 25M \times 6 \]

### Step 5: Set up the equation for total work.

Now, we can equate the total work done to the sum of the work done in the first 8 days and the work done in the next 6 days:
\[ (25M + 15W) \times 12 = (25M + 15W) \times 8 + 25M \times 6 \]

### Step 6: Simplify the equation.

Expanding both sides:
\[ 300M + 180W = 200M + 120W + 150M \]
\[ 300M + 180W = 350M + 120W \]

### Step 7: Rearranging the equation.

Rearranging gives:
\[ 180W - 120W = 350M - 300M \]
\[ 60W = 50M \]

### Step 8: Find the ratio of women's efficiency to men's efficiency.

From the equation \( 60W = 50M \):
\[ \frac{W}{M} = \frac{50}{60} = \frac{5}{6} \]

This means the efficiency of one woman is \( 5 \) and the efficiency of one man is \( 6 \).

### Step 9: Calculate the total work done.

Now, we can calculate the total work done:
\[ \text{Total Work} = (25 \times 6 + 15 \times 5) \times 12 \]
Calculating the efficiencies:
\[ = (150 + 75) \times 12 = 225 \times 12 = 2700 \text{ units of work} \]

### Step 10: Determine how long it will take for 15 women to complete the work.

The efficiency of 15 women is:
\[ 15W = 15 \times 5 = 75 \text{ units of work per day} \]

Now, to find the number of days \( D \) it will take for 15 women to complete the total work:
\[ D = \frac{\text{Total Work}}{\text{Efficiency of 15 women}} = \frac{2700}{75} = 36 \text{ days} \]

### Final Answer:
It will take 36 days for 15 women to complete the entire job.

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