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While working with 100% of his efficiency a man can complete a work in 20 days. In how many days can he complete the work while working with 25% efficiency?
- a)5
- b)20
- c)50
- d)80
Correct answer is option 'D'. Can you explain this answer?
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While working with 100% of his efficiency a man can complete a work in...
Understanding Work Efficiency
To solve the problem, we first need to understand how work efficiency is related to the time taken to complete a task.
Work Completion at 100% Efficiency
- A man can complete a certain work in 20 days when working at 100% efficiency.
- This means that he accomplishes 1/20 of the work in one day.
Calculating Work Completion at 25% Efficiency
- If the man works at 25% efficiency, he can complete only 25% of what he would at 100% efficiency in a day.
- Therefore, in one day at 25% efficiency, he completes:
\[
\frac{1}{20} \times 25\% = \frac{1}{20} \times \frac{25}{100} = \frac{1}{80}
\]
- This indicates that at 25% efficiency, the man completes 1/80 of the work in a single day.
Calculating Total Time Required
- To find out how many days he will take to complete the entire work at 25% efficiency, we can set up the equation:
\[
\text{Total Days} = \frac{\text{Total Work}}{\text{Work Done in One Day}} = \frac{1}{\frac{1}{80}} = 80
\]
- Hence, it will take him 80 days to complete the work while working at 25% efficiency.
Conclusion
- The correct answer is option D) 80 days.
This detailed breakdown clarifies how changes in efficiency impact the total time required to complete a task.
To solve the problem, we first need to understand how work efficiency is related to the time taken to complete a task.
Work Completion at 100% Efficiency
- A man can complete a certain work in 20 days when working at 100% efficiency.
- This means that he accomplishes 1/20 of the work in one day.
Calculating Work Completion at 25% Efficiency
- If the man works at 25% efficiency, he can complete only 25% of what he would at 100% efficiency in a day.
- Therefore, in one day at 25% efficiency, he completes:
\[
\frac{1}{20} \times 25\% = \frac{1}{20} \times \frac{25}{100} = \frac{1}{80}
\]
- This indicates that at 25% efficiency, the man completes 1/80 of the work in a single day.
Calculating Total Time Required
- To find out how many days he will take to complete the entire work at 25% efficiency, we can set up the equation:
\[
\text{Total Days} = \frac{\text{Total Work}}{\text{Work Done in One Day}} = \frac{1}{\frac{1}{80}} = 80
\]
- Hence, it will take him 80 days to complete the work while working at 25% efficiency.
Conclusion
- The correct answer is option D) 80 days.
This detailed breakdown clarifies how changes in efficiency impact the total time required to complete a task.
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While working with 100% of his efficiency a man can complete a work in...
Hence, Option D is correct.
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While working with 100% of his efficiency a man can complete a work in 20 days. In how many days can he complete the work while working with 25% efficiency?a)5b)20c)50d)80Correct answer is option 'D'. Can you explain this answer?
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