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12 men complete a work in 18 days. 6 days after they had started working, 4 men join them. Howmany more days will all of them take to complete the remaining work?
- a)10 days
- b)12 days
- c)15 days
- d)9 days
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
12 men complete a work in 18 days. 6 days after they had started worki...
12 × 18 = 12 × 6 + 16 × t Æ t = 9
Most Upvoted Answer
12 men complete a work in 18 days. 6 days after they had started worki...
Understanding the Work Rate
12 men can complete the work in 18 days. Therefore, the total work can be calculated as:
- Total Work = 12 men * 18 days = 216 man-days.
Work Completed in 6 Days
In the first 6 days, the 12 men work together to complete:
- Work Done = 12 men * 6 days = 72 man-days.
Remaining Work After 6 Days
The remaining work after 6 days is:
- Remaining Work = Total Work - Work Done = 216 man-days - 72 man-days = 144 man-days.
Work Rate After 4 Men Join
After 6 days, 4 more men join the original 12, making a total of 16 men.
- Work Rate of 16 men = 16 men/day.
Calculating Time to Complete Remaining Work
To find out how many days the 16 men will take to complete the remaining 144 man-days of work:
- Days Needed = Remaining Work / Work Rate = 144 man-days / 16 men = 9 days.
Conclusion
Thus, after the initial 6 days of work, the 16 men will take an additional 9 days to finish the remaining work. Hence, the correct answer is option 'D'.
12 men can complete the work in 18 days. Therefore, the total work can be calculated as:
- Total Work = 12 men * 18 days = 216 man-days.
Work Completed in 6 Days
In the first 6 days, the 12 men work together to complete:
- Work Done = 12 men * 6 days = 72 man-days.
Remaining Work After 6 Days
The remaining work after 6 days is:
- Remaining Work = Total Work - Work Done = 216 man-days - 72 man-days = 144 man-days.
Work Rate After 4 Men Join
After 6 days, 4 more men join the original 12, making a total of 16 men.
- Work Rate of 16 men = 16 men/day.
Calculating Time to Complete Remaining Work
To find out how many days the 16 men will take to complete the remaining 144 man-days of work:
- Days Needed = Remaining Work / Work Rate = 144 man-days / 16 men = 9 days.
Conclusion
Thus, after the initial 6 days of work, the 16 men will take an additional 9 days to finish the remaining work. Hence, the correct answer is option 'D'.
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