If 'b' men can do a piece of work in 'c' days, then the number of days taken by 'd' men to do `(1)/(m)`th of the same piece of work be

Options

A. `(bc)/(d+m)`
B. `(bc)/(dm)`
C. `(b+c)/(d+m)`
D. `(b+c)/(dm)`

Answer

To solve the problem, we need to determine how many days 'd' men will take to complete \(\frac{1}{m}\)th of the work that 'b' men can complete in 'c' days. Let's break this down step by step.

### Step-by-Step Solution:

1. **Understand the Work Rate of 'b' Men:**
- If 'b' men can complete the entire work in 'c' days, then the total work can be expressed in man-days as:
\[ \text{Total Work} = b \times c \text{ man-days} \]

2. **Calculate the Work Done by 'd' Men:**
- The work done by 'd' men in one day is:
\[ \text{Work done by } d \text{ men in one day} = d \text{ man-days} \]

3. **Determine the Work to be Done:**
- We are interested in \(\frac{1}{m}\)th of the total work. Therefore, the work to be done is:
\[ \text{Work to be done} = \frac{1}{m} \times (b \times c) = \frac{bc}{m} \text{ man-days} \]

4. **Calculate the Number of Days Taken by 'd' Men:**
- To find the number of days 'd' men take to complete \(\frac{bc}{m}\) man-days of work, we use the formula:
\[ \text{Number of Days} = \frac{\text{Total Work}}{\text{Work done per day}} = \frac{\frac{bc}{m}}{d} \]

5. **Simplify the Expression:**
- This simplifies to:
\[ \text{Number of Days} = \frac{bc}{md} \]

### Final Answer:
The number of days taken by 'd' men to do \(\frac{1}{m}\)th of the same piece of work is:
\[ \frac{bc}{md} \]