Question

In 25 days, 30 men complete 15 projects. In how many days can 14 men complete 7 projects?

• A. 21 days
• B. 25 days
• C. 50 days
• D. 32 days

Hint:

When dealing with such problems, always use the man-days concept (men × days = total work) to break down and calculate the total number of days needed.

Answer 1

The Correct Option is B

We know the relationship of man-days, i.e., the number of men times the number of days needed to complete a project. Step 1: Find the total man-days for 15 projects
\text{Man-days required for 15 projects} = 30 \times 25 = 750 \text{ man-days for 15 projects.}

Step 2: Find the man-days required for 1 project
\text{Man-days for 1 project} = \( \frac{750}{15} \) = 50 \text{ man-days per project.}

Step 3: Calculate how many days 14 men will take to complete 7 projects
\text{Man-days for 7 projects} = 7 \times 50 = 350 \text{ man-days for 7 projects.}
\text{Now, for 14 men:}
\text{Days required} = \( \frac{350}{14} \) = 25 \text{ days.}

Step 4: Final Answer
Thus, 14 men will complete 7 projects in 25 days. Final Answer: The correct answer is (b) 25 days.