Question

A house is built by 20 workers in 30 days. How many workers will be needed to complete the work in 15 days?

• A. 20
• B. 34
• C. 40
• D. 45
• E. 52

Hint:

For inverse proportion problems, you can also use reasoning. The time is halved (from 30 days to 15 days), so the number of workers must be doubled to get the same amount of work done. Double 20 workers is 40 workers.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a classic inverse proportion problem. The total amount of work is constant. The number of workers is inversely proportional to the number of days required to complete the work. This means if you decrease the time, you must increase the number of workers.
Step 2: Key Formula or Approach:
The total work done can be measured in "worker-days".
Total Work = (Number of Workers) \(\times\) (Number of Days)
Let \(W_1\) and \(D_1\) be the initial number of workers and days, and \(W_2\) and \(D_2\) be the new number of workers and days. Since the total work is the same:
\[ W_1 \times D_1 = W_2 \times D_2 \] Step 3: Detailed Explanation:
We are given the initial conditions:
\(W_1 = 20\) workers
\(D_1 = 30\) days
First, calculate the total work required to build the house in worker-days:
\[ \text{Total Work} = 20 \text{ workers} \times 30 \text{ days} = 600 \text{ worker-days} \] Now, we need to complete this same amount of work in a different number of days:
\(D_2 = 15\) days
We need to find the number of workers, \(W_2\), required. Using the formula:
\[ \text{Total Work} = W_2 \times D_2 \] \[ 600 = W_2 \times 15 \] Solve for \(W_2\):
\[ W_2 = \frac{600}{15} \] To simplify the division: \(600/15 = (60 \times 10) / 15 = 4 \times 10 = 40\).
\[ W_2 = 40 \] So, 40 workers will be needed to complete the work in 15 days.
Step 4: Final Answer:
40 workers will be needed.