24 workers can build a wall in 15 days. How many days will 9 workers take to build a similar wall?

Options

A. 30 days
B. 40 days
C. 50 days
D. 60 days

Answer

To solve the problem step by step, we can use the concept of inverse proportionality between the number of workers and the time taken to complete the work.

### Step 1: Determine the total work done in worker-days
First, we calculate the total amount of work done in worker-days by the 24 workers in 15 days.

\[ \text{Total work} = \text{Number of workers} \times \text{Number of days} = 24 \text{ workers} \times 15 \text{ days} = 360 \text{ worker-days} \]

### Step 2: Calculate the time taken by 9 workers
Now, we need to find out how many days it will take for 9 workers to complete the same amount of work (360 worker-days).

Let \( x \) be the number of days it will take for 9 workers to finish the work. We can set up the equation:

\[ \text{Total work} = \text{Number of workers} \times \text{Number of days} \]

Substituting the values we have:

\[ 360 \text{ worker-days} = 9 \text{ workers} \times x \text{ days} \]

### Step 3: Solve for \( x \)
Now, we can solve for \( x \):

\[ x = \frac{360 \text{ worker-days}}{9 \text{ workers}} = 40 \text{ days} \]

### Conclusion
Thus, 9 workers will take **40 days** to build a similar wall.

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