40 mechanics can repair a bike in 56 days. In how many days 32 mechanics will do the same work?

Options

A. 60 days
B. 56 days
C. 80 days
D. 70 days

Answer

To solve the problem, we need to determine how many days 32 mechanics will take to repair the bike, given that 40 mechanics can do it in 56 days.

### Step-by-Step Solution:

1. **Calculate the total work done in terms of "mechanic-days":**
- If 40 mechanics can complete the work in 56 days, we can calculate the total work in mechanic-days.
- Total work = Number of mechanics × Number of days
- Total work = 40 mechanics × 56 days = 2240 mechanic-days.

2. **Determine the number of days required for 32 mechanics to complete the same work:**
- Let the number of days required for 32 mechanics to complete the work be \( x \).
- The total work done by 32 mechanics in \( x \) days will also be expressed in mechanic-days:
- Total work = Number of mechanics × Number of days
- Total work = 32 mechanics × \( x \) days.

3. **Set up the equation:**
- Since the total work is the same, we can set the two expressions for total work equal to each other:
\[ 32x = 2240 \]

4. **Solve for \( x \):**
- To find \( x \), divide both sides of the equation by 32:
\[ x = \frac{2240}{32} \]
- Calculating the right side:
\[ x = 70 \]

5. **Conclusion:**
- Therefore, 32 mechanics will take 70 days to repair the bike.

### Final Answer:
32 mechanics will take **70 days** to repair the bike.