15 men can do a work in 20 days. How many days will 10 men take to do double the same work0

Options

A. 40
B. 60
C. 50
D. 30

Answer

To solve the problem step by step, we will use the concept of work done, which is calculated using the formula:

\[ \text{Work} = \text{Men} \times \text{Days} \]

### Step 1: Calculate the total work done by 15 men in 20 days
Given that 15 men can complete the work in 20 days, we can calculate the total work (W) as follows:

\[ W = \text{Men} \times \text{Days} = 15 \times 20 = 300 \text{ man-days} \]

### Step 2: Determine the total work for double the original work
Since we need to find out how many days it will take for 10 men to do double the same work, we first calculate the total work for double the original work:

\[ \text{Total Work for double the work} = 2W = 2 \times 300 = 600 \text{ man-days} \]

### Step 3: Set up the equation for 10 men
Now, we need to find out how many days (let's denote it as X) it will take for 10 men to complete 600 man-days of work. We can set up the equation as follows:

\[ \text{Work} = \text{Men} \times \text{Days} \]

Substituting the known values:

\[ 600 = 10 \times X \]

### Step 4: Solve for X
Now, we can solve for X:

\[ X = \frac{600}{10} = 60 \text{ days} \]

### Conclusion
Therefore, 10 men will take 60 days to complete double the same work.