24 men can repair a road in 50 days. If they are joined by 16 more men, then in how much time (in days) the road can be repaired?

Options

A. 28
B. 25
C. 32
D. 30

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total work done in man-days
We know that 24 men can repair the road in 50 days. Therefore, the total work can be calculated in terms of man-days.

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 24 \text{ men} \times 50 \text{ days} = 1200 \text{ man-days} \]

### Step 2: Determine the total number of men after adding more workers
Initially, there are 24 men. If 16 more men join, the total number of men becomes:

\[ \text{Total Number of Men} = 24 + 16 = 40 \text{ men} \]

### Step 3: Calculate the number of days required for 40 men to complete the same work
Now, we need to find out how many days it will take for 40 men to complete the same amount of work (1200 man-days).

Let \( D \) be the number of days required for 40 men to complete the work. The equation for the total work in man-days can be set up as follows:

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \]
\[ 1200 \text{ man-days} = 40 \text{ men} \times D \text{ days} \]

### Step 4: Solve for \( D \)
Rearranging the equation to solve for \( D \):

\[ D = \frac{1200 \text{ man-days}}{40 \text{ men}} = 30 \text{ days} \]

### Conclusion
Thus, if 16 more men join the original 24 men, the road can be repaired in **30 days**.

---