Question

If 5 workers can complete a job in 12 days, how long will 8 workers take to complete the same job (assuming all work at the same rate)?

• A. 6 days
• B. 7.5 days
• C. 8 days
• D. 9 days

Hint:

For work problems, use the formula: \(\text{Workers} \times \text{Days} = \text{Constant}\). More workers reduce the time proportionally.

Answer 1

The Correct Option is B

To solve the problem, we need to find out how long 8 workers will take to complete a job that 5 workers can finish in 12 days, assuming all workers work at the same rate.

1. Understanding the Concepts:

- Work: The total amount of job to be done is fixed.
- Number of workers (n): The people working on the job.
- Time (T): The duration needed to complete the job.
- Work Rate: Amount of work done by one worker in one day.
- More workers can complete the job faster, so the time taken is inversely proportional to the number of workers if the work rate is constant.

2. Given Values:

\( n_1 = 5 \) workers
\( T_1 = 12 \) days (time taken by 5 workers)
\( n_2 = 8 \) workers
\( T_2 = ? \) (time taken by 8 workers)

3. Step-by-step Solution:

Step 1: Calculate the total work in terms of worker-days.
Since 5 workers complete the job in 12 days, total work = number of workers × time = \( 5 \times 12 = 60 \) worker-days.
This means the job requires 60 days of work done by one worker.

Step 2: Find how many days 8 workers will take to complete the same total work.
If 8 workers work together, each day they complete 8 worker-days of work.
So, total days required = \( \frac{\text{Total work}}{\text{Number of workers}} = \frac{60}{8} = 7.5 \) days.

4. Interpretation:

The 8 workers can finish the job faster than 5 workers. Specifically, they will take 7 and a half days, which is 7 days and 12 hours.

Final Answer:

8 workers will take 7.5 days to complete the job.