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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?
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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DIRECTIONS for the question: Solve the following question and mark the...
Time taken by a person to complete 1 job = 120
Work done by a person in 1 day = 1/120
Work done on 2nd day by 2 persons of same efficiency = 1/120 + 2/120 = 3/120
Work done on 3rd day by 3 persons . of same efficiency = 1/120 + 2/120 + 3/120 = 6/120
Work done on nth day by n persons of same efficiency = (1+2+3+4....... + n)/120
1 Job is completed on nth day. So the work done will be equal to 1:
(1+2+3+4....... + n)/120 = 1
n(n+1)/2 = 120 ( Sum of 1st n natural numbers = n(n+1)/2 )
Substituting the values from the options, we'll get n=15
Work done by a person in 1 day = 1/120
Work done on 2nd day by 2 persons of same efficiency = 1/120 + 2/120 = 3/120
Work done on 3rd day by 3 persons . of same efficiency = 1/120 + 2/120 + 3/120 = 6/120
Work done on nth day by n persons of same efficiency = (1+2+3+4....... + n)/120
1 Job is completed on nth day. So the work done will be equal to 1:
(1+2+3+4....... + n)/120 = 1
n(n+1)/2 = 120 ( Sum of 1st n natural numbers = n(n+1)/2 )
Substituting the values from the options, we'll get n=15
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DIRECTIONS for the question: Solve the following question and mark the...
Explanation:
Let's consider the work done by the first person on Day 1 as 'x'.
Thus, the total work is '120x'.
Calculation:
Day 1: One person works, so work done = x. Remaining work = 120x - x = 119x.
Day 2: Two people work, so work done = 2x. Remaining work = 119x - 2x = 117x.
Day 3: Three people work, so work done = 3x. Remaining work = 117x - 3x = 114x.
Similarly, we can calculate the work done and remaining work for each day.
Day 4: 4 people work, work done = 4x, remaining work = 111x.
Day 5: 5 people work, work done = 5x, remaining work = 106x.
Day 6: 6 people work, work done = 6x, remaining work = 100x.
Day 7: 7 people work, work done = 7x, remaining work = 93x.
Day 8: 8 people work, work done = 8x, remaining work = 85x.
Day 9: 9 people work, work done = 9x, remaining work = 76x.
Day 10: 10 people work, work done = 10x, remaining work = 66x.
Day 11: 11 people work, work done = 11x, remaining work = 55x.
Day 12: 12 people work, work done = 12x, remaining work = 43x.
Day 13: 13 people work, work done = 13x, remaining work = 30x.
Day 14: 14 people work, work done = 14x, remaining work = 16x.
Day 15: 15 people work, work done = 15x, remaining work = 1x.
Conclusion:
On Day 15, when 15 people work on the job, the remaining work is only '1x', which means the work is completed. Therefore, the job will be completed in '15' days.
Let's consider the work done by the first person on Day 1 as 'x'.
Thus, the total work is '120x'.
Calculation:
Day 1: One person works, so work done = x. Remaining work = 120x - x = 119x.
Day 2: Two people work, so work done = 2x. Remaining work = 119x - 2x = 117x.
Day 3: Three people work, so work done = 3x. Remaining work = 117x - 3x = 114x.
Similarly, we can calculate the work done and remaining work for each day.
Day 4: 4 people work, work done = 4x, remaining work = 111x.
Day 5: 5 people work, work done = 5x, remaining work = 106x.
Day 6: 6 people work, work done = 6x, remaining work = 100x.
Day 7: 7 people work, work done = 7x, remaining work = 93x.
Day 8: 8 people work, work done = 8x, remaining work = 85x.
Day 9: 9 people work, work done = 9x, remaining work = 76x.
Day 10: 10 people work, work done = 10x, remaining work = 66x.
Day 11: 11 people work, work done = 11x, remaining work = 55x.
Day 12: 12 people work, work done = 12x, remaining work = 43x.
Day 13: 13 people work, work done = 13x, remaining work = 30x.
Day 14: 14 people work, work done = 14x, remaining work = 16x.
Day 15: 15 people work, work done = 15x, remaining work = 1x.
Conclusion:
On Day 15, when 15 people work on the job, the remaining work is only '1x', which means the work is completed. Therefore, the job will be completed in '15' days.
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DIRECTIONS for the question: Solve the following question and mark the best possible option.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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DIRECTIONS for the question: Solve the following question and mark the best possible option.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 DIRECTIONS for the question: Solve the following question and mark the best possible option.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 DIRECTIONS for the question: Solve the following question and mark the best possible option.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?.
DIRECTIONS for the question: Solve the following question and mark the best possible option.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 DIRECTIONS for the question: Solve the following question and mark the best possible option.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 DIRECTIONS for the question: Solve the following question and mark the best possible option.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?.
Solutions for DIRECTIONS for the question: Solve the following question and mark the best possible option.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? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of DIRECTIONS for the question: Solve the following question and mark the best possible option.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? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONS for the question: Solve the following question and mark the best possible option.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?, a detailed solution for DIRECTIONS for the question: Solve the following question and mark the best possible option.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? has been provided alongside types of DIRECTIONS for the question: Solve the following question and mark the best possible option.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? theory, EduRev gives you an
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