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The efficiency of Nitish is 80% more than Paras and Paras takes 45 days to complete a piece of work. Nitish started work alone and then Paras joined him 9 days before the actual completion of work. For how many days Nitish worked alone?
- a)20
- b)15
- c)11
- d)17
- e)12
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The efficiency of Nitish is 80% more than Paras and Paras takes 45 da...
Given:
- Efficiency of Nitish is 80% more than Paras.
- Paras takes 45 days to complete a piece of work.
- Nitish started work alone and Paras joined him 9 days before the actual completion of work.
To find:
For how many days Nitish worked alone.
Solution:
Let's assume that Nitish takes 'x' days to complete the work alone.
Efficiency:
- Efficiency is inversely proportional to the number of days taken to complete the work.
- Let's calculate the efficiency of Paras and Nitish.
Efficiency of Paras = 1/45 (as Paras takes 45 days to complete the work)
Efficiency of Nitish = 1/x (as Nitish takes x days to complete the work)
Efficiency of Nitish = Efficiency of Paras + 80% of Efficiency of Paras
=> 1/x = 1/45 + 80/100 * 1/45
=> 1/x = 1/45 + 4/45
=> 1/x = 5/45
=> 1/x = 1/9
=> x = 9
Therefore, Nitish takes 9 days to complete the work alone.
Finding the number of days Nitish worked alone:
- Paras joined Nitish 9 days before the actual completion of work.
- So, the total number of days taken to complete the work is x+9.
Since Nitish takes 9 days to complete the work alone, he worked alone for x-9 days.
Substituting the value of x from previous calculation,
Nitish worked alone for 9-9 = 0 days.
Therefore, Nitish worked alone for 0 days.
Conclusion:
Nitish worked alone for 0 days.
- Efficiency of Nitish is 80% more than Paras.
- Paras takes 45 days to complete a piece of work.
- Nitish started work alone and Paras joined him 9 days before the actual completion of work.
To find:
For how many days Nitish worked alone.
Solution:
Let's assume that Nitish takes 'x' days to complete the work alone.
Efficiency:
- Efficiency is inversely proportional to the number of days taken to complete the work.
- Let's calculate the efficiency of Paras and Nitish.
Efficiency of Paras = 1/45 (as Paras takes 45 days to complete the work)
Efficiency of Nitish = 1/x (as Nitish takes x days to complete the work)
Efficiency of Nitish = Efficiency of Paras + 80% of Efficiency of Paras
=> 1/x = 1/45 + 80/100 * 1/45
=> 1/x = 1/45 + 4/45
=> 1/x = 5/45
=> 1/x = 1/9
=> x = 9
Therefore, Nitish takes 9 days to complete the work alone.
Finding the number of days Nitish worked alone:
- Paras joined Nitish 9 days before the actual completion of work.
- So, the total number of days taken to complete the work is x+9.
Since Nitish takes 9 days to complete the work alone, he worked alone for x-9 days.
Substituting the value of x from previous calculation,
Nitish worked alone for 9-9 = 0 days.
Therefore, Nitish worked alone for 0 days.
Conclusion:
Nitish worked alone for 0 days.
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Community Answer
The efficiency of Nitish is 80% more than Paras and Paras takes 45 da...
Paras alone can complete a piece of work in 45 days
⇒ Paras's one-day work = 1/45
Nitish is 80% more efficient than Paras,
Let the total job is completed in T days, then
Part of work done = Number of days of work × One day's work
Nitish worked for T days, so Nitish work = (T/25)
Paras's worked for only 9 days, so Paras work = (9/45)
Nitish's work + Paras's work = 1 (∵ Work is completed)
∴ Nitish worked alone for = 20 - 9 = 11 days
Hence, the correct option is (C).
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The efficiency of Nitish is 80% more than Paras and Paras takes 45 days to complete a piece of work. Nitish started work alone and then Paras joined him 9 days before the actual completion of work. For how many days Nitish worked alone?a)20b)15c)11d)17e)12Correct answer is option 'C'. Can you explain this answer?
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