If m men can do a work in r days, then the number of days taken by `(m+n)` men to do it is :

Options

A. `(m+n)/(mn)`
B. `(m+n)/(mr)`
C. `(mr)/(m+n)`
D. `((m+n)r)/(mn)`

Answer

To solve the problem, we need to determine how many days it will take for (m+n) men to complete the same work that m men can do in r days.

### Step-by-Step Solution:

1. **Calculate the total work done by m men in r days:**
- If m men can complete the work in r days, the total work (W) can be expressed in terms of man-days.
- Total work \( W = m \times r \) (man-days).

2. **Determine the work done by (m+n) men in one day:**
- If (m+n) men are working, the amount of work they can do in one day is \( m+n \).

3. **Calculate the number of days taken by (m+n) men to complete the work:**
- Let the number of days taken by (m+n) men to complete the work be \( D \).
- The total work done by (m+n) men in \( D \) days is \( (m+n) \times D \).
- Since the total work is the same, we can set up the equation:
\[ (m+n) \times D = m \times r \]

4. **Solve for D:**
- Rearranging the equation gives:
\[ D = \frac{m \times r}{m+n} \]

### Final Answer:
The number of days taken by (m+n) men to complete the work is:
\[ D = \frac{m \times r}{m+n} \]