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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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A person can complete a job in 120 days. He works alone on Day 1. On D...
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.
120x = x * n(n+1)/2
n2 + n – 240 = 0
n = 15 is the only positive solution.
Hence, it takes 15 days to complete the work.
Most Upvoted Answer
A person can complete a job in 120 days. He works alone on Day 1. On D...
Explanation:
Day-wise calculation:
- On Day 1, 1 person completes 1/120 of the job.
- On Day 2, 2 people complete 2/120 of the job.
- On Day 3, 3 people complete 3/120 of the job.
- Similarly, on Day 4, 4 people complete 4/120 of the job.
Pattern observation:
- The total work is divided into 120 equal parts.
- On each day, the number of people working is equal to the day number.
- So, the work completed each day will be the sum of the fractions completed by the people on that day.
Calculating total days:
- To find the total number of days required to complete the job, we need to find the day on which the total work is completed.
- The sum of the fractions completed each day is a series of consecutive natural numbers i.e. 1+2+3+...+n.
- The sum of the first n natural numbers is n*(n+1)/2.
- Equating this to 120, we get n*(n+1)/2 = 120.
- Solving this equation, we get n = 15.
Therefore, it will take 15 days to complete the job when each day a new person joins the work with the same efficiency.
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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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