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A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?
Correct answer is '15'. Can you explain this answer?
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Most Upvoted Answer
A person can complete a job in 120 days. He works alone on Day 1. On ...
Explanation:
To solve this problem, let's break it down step by step.
Day 1:
- Only one person is working on the job, so the work done on Day 1 is 1/120th of the job.
Day 2:
- On Day 2, two people are working on the job. Each person can complete the job in 120 days, so together they can complete 2/120th or 1/60th of the job in one day.
- The total work done on Day 1 and Day 2 is 1/120 + 1/60 = 1/80th of the job.
Day 3:
- On Day 3, three people are working on the job. Each person can complete the job in 120 days, so together they can complete 3/120th or 1/40th of the job in one day.
- The total work done on Day 1, Day 2, and Day 3 is 1/120 + 1/60 + 1/40 = 1/30th of the job.
General Pattern:
- We can observe that each day, the number of people working on the job is equal to the number of days that have passed.
- The work done by each person in one day remains constant at 1/120th of the job.
- Therefore, on Day n, n people are working on the job, and together they can complete n/120th of the job in one day.
Calculating the Total Work Done:
- To find the total work done, we need to sum up the work done on each day.
- The sum of the series 1/120 + 2/120 + 3/120 + ... + n/120 is given by the formula n(n+1)/2*120.
- We need to find the smallest value of n for which the sum is equal to or greater than 1 (the entire job).
Calculating the Number of Days:
- Setting the sum equal to 1 and solving the equation n(n+1)/2*120 = 1, we get n^2 + n - 240 = 0.
- Solving this quadratic equation, we find that n = 15.
- Therefore, it will take 15 days to complete the job.
Conclusion:
Thus, it will take 15 days to complete the job when a new person with the same efficiency joins the work every day.
To solve this problem, let's break it down step by step.
Day 1:
- Only one person is working on the job, so the work done on Day 1 is 1/120th of the job.
Day 2:
- On Day 2, two people are working on the job. Each person can complete the job in 120 days, so together they can complete 2/120th or 1/60th of the job in one day.
- The total work done on Day 1 and Day 2 is 1/120 + 1/60 = 1/80th of the job.
Day 3:
- On Day 3, three people are working on the job. Each person can complete the job in 120 days, so together they can complete 3/120th or 1/40th of the job in one day.
- The total work done on Day 1, Day 2, and Day 3 is 1/120 + 1/60 + 1/40 = 1/30th of the job.
General Pattern:
- We can observe that each day, the number of people working on the job is equal to the number of days that have passed.
- The work done by each person in one day remains constant at 1/120th of the job.
- Therefore, on Day n, n people are working on the job, and together they can complete n/120th of the job in one day.
Calculating the Total Work Done:
- To find the total work done, we need to sum up the work done on each day.
- The sum of the series 1/120 + 2/120 + 3/120 + ... + n/120 is given by the formula n(n+1)/2*120.
- We need to find the smallest value of n for which the sum is equal to or greater than 1 (the entire job).
Calculating the Number of Days:
- Setting the sum equal to 1 and solving the equation n(n+1)/2*120 = 1, we get n^2 + n - 240 = 0.
- Solving this quadratic equation, we find that n = 15.
- Therefore, it will take 15 days to complete the job.
Conclusion:
Thus, it will take 15 days to complete the job when a new person with the same efficiency joins the work every day.
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Community Answer
A person can complete a job in 120 days. He works alone on Day 1. On ...
Let the rate of work of a person be x units/day. Hence, the total work = 120x.
It is given that one first day, one person works, on the second day two people work and so on.
Hence, the work done on day 1, day 2,... will be x, 2x, 3x, ... respectively.
The sum should be equal to 120x.
n2 + n − 240 = 0
n = 15 is the only positive solution.
Hence, it takes 15 days to complete the work.
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A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?Correct answer is '15'. Can you explain this answer?
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