21 workers can repair a road in 40 days. If they are joined by 7 more workers, then in how much time (in days) the road can be repaired?

Options

A. 27
B. 28
C. 30
D. 32

Answer

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

### Step 1: Calculate the total work done by the initial workers
We know that 21 workers can repair a road in 40 days. We can calculate the total work done in terms of worker-days.

\[ \text{Total Work} = \text{Number of Workers} \times \text{Days} = 21 \text{ workers} \times 40 \text{ days} = 840 \text{ worker-days} \]

**Hint:** To find total work, multiply the number of workers by the number of days they work.

### Step 2: Determine the new total number of workers
After 7 more workers join, the total number of workers becomes:

\[ \text{Total Workers} = 21 + 7 = 28 \text{ workers} \]

**Hint:** Simply add the new workers to the existing number of workers to find the total.

### Step 3: Calculate the time taken to complete the work with the new number of workers
Now, we need to find out how many days it will take for 28 workers to complete the same amount of work (840 worker-days). We use the formula:

\[ \text{Days} = \frac{\text{Total Work}}{\text{Number of Workers}} = \frac{840 \text{ worker-days}}{28 \text{ workers}} \]

Calculating this gives:

\[ \text{Days} = \frac{840}{28} = 30 \text{ days} \]

**Hint:** To find the number of days, divide the total work by the number of workers.

### Conclusion
Thus, if 21 workers are joined by 7 more workers, the road can be repaired in **30 days**.

**Final Answer:** 30 days