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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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Verified Answer
A person can complete a job in 120 days. He works alone on Day 1. On D...
We can see that,
On Day 1, the person works alone.
On Day 1, the person works alone.
So, work done on Day 1 = 1/120
Next day, another person joins him, Work done on Day 2 = 2/120
And so on, until the final day
So, sum total of work done = 1/120 + 2/120 +………+ n/120 = 1
(1/120) (1 + 2+3+……+n) = 1
(1/120) [n(n+1)/2] = 1 (Sum of n positive integers)
On solving, we get n = 15.
And so on, until the final day
So, sum total of work done = 1/120 + 2/120 +………+ n/120 = 1
(1/120) (1 + 2+3+……+n) = 1
(1/120) [n(n+1)/2] = 1 (Sum of n positive integers)
On solving, we get n = 15.
Most Upvoted Answer
A person can complete a job in 120 days. He works alone on Day 1. On D...
Efficiency of Each Worker:
- Each worker has the same efficiency.
- Each worker can complete the job in 120 days.
Working Alone:
- On Day 1, only one person is working.
- This person can complete the job in 120 days.
Working Together:
- On Day 2, two people are working together.
- Each person can complete the job in 120 days.
- Therefore, their combined efficiency is doubled.
- The job can be completed in half the time, i.e., 60 days.
Pattern:
- Each day, a new person joins the work.
- The number of people working together increases by one each day.
- The efficiency of the team increases accordingly.
Calculating the Number of Days:
- On Day 1, one person works alone and completes 1/120th of the job.
- On Day 2, two people work together and complete another 1/120th of the job.
- On Day 3, three people work together and complete another 1/120th of the job.
- This pattern continues.
Summing Up the Progress:
- On Day 1, 1/120th of the job is completed.
- On Day 2, 1/120th + 1/120th = 2/120th = 1/60th of the job is completed.
- On Day 3, 1/120th + 1/120th + 1/120th = 3/120th = 1/40th of the job is completed.
- This pattern continues.
Calculating the Total Time:
- The job will be completed when the sum of the progress is equal to 1.
- Setting up an equation: 1/120 + 1/60 + 1/40 + ... = 1
- Simplifying the equation: 1/120 + (2/120) + (3/120) + ... = 1
- The sum of the series can be written as: 1/120 * (1 + 2 + 3 + ...)
- The sum of the series 1 + 2 + 3 + ... = n(n+1)/2, where n is the number of days.
- Substituting the values: 1/120 * n(n+1)/2 = 1
- Simplifying the equation: n(n+1) = 240
- Solving the quadratic equation: n^2 + n - 240 = 0
- Factoring the equation: (n - 15)(n + 16) = 0
- The positive solution is n = 15.
Thus, it will take 15 days to complete the job.
- Each worker has the same efficiency.
- Each worker can complete the job in 120 days.
Working Alone:
- On Day 1, only one person is working.
- This person can complete the job in 120 days.
Working Together:
- On Day 2, two people are working together.
- Each person can complete the job in 120 days.
- Therefore, their combined efficiency is doubled.
- The job can be completed in half the time, i.e., 60 days.
Pattern:
- Each day, a new person joins the work.
- The number of people working together increases by one each day.
- The efficiency of the team increases accordingly.
Calculating the Number of Days:
- On Day 1, one person works alone and completes 1/120th of the job.
- On Day 2, two people work together and complete another 1/120th of the job.
- On Day 3, three people work together and complete another 1/120th of the job.
- This pattern continues.
Summing Up the Progress:
- On Day 1, 1/120th of the job is completed.
- On Day 2, 1/120th + 1/120th = 2/120th = 1/60th of the job is completed.
- On Day 3, 1/120th + 1/120th + 1/120th = 3/120th = 1/40th of the job is completed.
- This pattern continues.
Calculating the Total Time:
- The job will be completed when the sum of the progress is equal to 1.
- Setting up an equation: 1/120 + 1/60 + 1/40 + ... = 1
- Simplifying the equation: 1/120 + (2/120) + (3/120) + ... = 1
- The sum of the series can be written as: 1/120 * (1 + 2 + 3 + ...)
- The sum of the series 1 + 2 + 3 + ... = n(n+1)/2, where n is the number of days.
- Substituting the values: 1/120 * n(n+1)/2 = 1
- Simplifying the equation: n(n+1) = 240
- Solving the quadratic equation: n^2 + n - 240 = 0
- Factoring the equation: (n - 15)(n + 16) = 0
- The positive solution is n = 15.
Thus, it will take 15 days to complete the job.
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Community Answer
A person can complete a job in 120 days. He works alone on Day 1. On D...
Work by one person in one day- 1/120
work by 2 persons on 2nd day- 2/120
similarly, in proceeding days the same way used to calculate and we get--- 1/120+2/120+3/120...n/120.
So, 1/120 (1+2+3....n)
= 1/120 [n(n+1)/2]
=15 or -16 = 15 days.
work by 2 persons on 2nd day- 2/120
similarly, in proceeding days the same way used to calculate and we get--- 1/120+2/120+3/120...n/120.
So, 1/120 (1+2+3....n)
= 1/120 [n(n+1)/2]
=15 or -16 = 15 days.
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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 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? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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