Question

A contractor employed a certain number of workers to complete a project in 100 days. However, after 25 days, he found that only one-third of the work had been completed. How many additional workers must he employ so that the project can be completed on time?

• A. 25
• B. 30
• C. 35
• D. 40
• E. None of the above

Hint:

In work and time problems, always compare expected progress with actual progress. If actual work>expected, no extra workers are required; if actual<expected, calculate shortfall and proportionally add more workers.

Answer 1

The Correct Option is B

Step 1: Represent total work.
Let the total work required for the project be equal to 1 unit (100%).
The work must be completed in 100 days.
Step 2: Work done in first 25 days.
It is given that only one-third of the work has been completed in 25 days.
So, work completed = \( \tfrac{1}{3} \).
Work remaining = \( 1 - \tfrac{1}{3} = \tfrac{2}{3} \).
Step 3: Determine actual capacity of existing workers.
If in 25 days, the workers can do one-third of the work, then in 100 days, they would have completed \[ \frac{100}{25} \times \frac{1}{3} = 4 \times \frac{1}{3} = \frac{4}{3}>1 \] Wait: Let’s carefully recalculate.
- In 25 days → work done = 1/3.
- So, in 1 day → work done = 1/75.
- In 100 days → total work possible = 100 × (1/75) = 4/3.
This shows the workers’ capacity is to finish the job in less than 100 days if they continue. But we must double-check.
Step 4: Re-examine the requirement.
Work done in 25 days = 1/3.
Work remaining = 2/3.
Time remaining = 100 − 25 = 75 days.
If the same workforce continues, in 75 days, they would complete
= (75/25) × (1/3) = 3 × (1/3) = 1.
That means they will finish exactly on time.
So there is no need for extra workers.
But wait — let us verify with the intended question logic. Sometimes such questions assume "less than expected progress" and ask for extra manpower.
Step 5: Adjust interpretation.
Expected work in 25 days = 25% of project.
Actual work done = 33.33%.
Since more work is completed than expected, no additional workers are required.
Hence, the correct answer is "None of the above".
Step 6: Conclude.
The project can be completed on time with the existing workforce. No extra workers are required. \[ \boxed{\text{None of the above (Option E)}} \]