Question

12 Men can complete a work in 20 days. Working after 5 days, 6 men left. In how many more days will the remaining work be completed by the remaining 6 Men?

• A. 35 days
• B. 30 days
• C. 25 days
• D. 32 days

Hint:

After 5 days, the 12 men have enough work left for another 15 days (\(12 \times 15\) man-days).
Since the workforce is halved (from 12 men to 6 men), the time taken to complete the remaining work must double:
\(15 \text{ days} \times 2 = 30 \text{ days}\). No heavy calculation is needed!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question belongs to the topic of Time and Work, focusing on the concepts of man-days and workforce changes during a project.

Step 2: Key Formulas and approach:
The total work can be represented in terms of "man-days", which is the product of the number of men and the number of days they work:
\[ \text{Total Work} = \text{Men} \times \text{Days} \] We calculate the total man-days required, subtract the work already completed in the first 5 days, and then find how many days the remaining reduced workforce needs to finish the rest.

Step 3: Detailed Explanation:

• Compute the total work capacity required:
\[ \text{Total Work} = 12 \text{ men} \times 20 \text{ days} = 240 \text{ man-days} \]

• Work completed by the 12 men during the first 5 days:
\[ \text{Work Done} = 12 \text{ men} \times 5 \text{ days} = 60 \text{ man-days} \]

• Compute the remaining work left to be completed:
\[ \text{Remaining Work} = 240 - 60 = 180 \text{ man-days} \]

• Determine the remaining workforce after 6 men leave:
\[ \text{Remaining Men} = 12 - 6 = 6 \text{ men} \]

• Calculate the additional days required by these 6 men to finish the 180 man-days of remaining work:
\[ \text{Additional Days} = \frac{\text{Remaining Work}}{\text{Remaining Men}} = \frac{180 \text{ man-days}}{6 \text{ men}} = 30 \text{ days} \]

Step 4: Final Answer:
The remaining work will be completed by the remaining men in \(30\) additional days, corresponding to Option (B).