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DIRECTIONS for questions: Select the correct alternative from the given choices.
M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.
- a)8
- b)9
- c)10
- d)7
Correct answer is option 'A'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the giv...
Part of the job doneonthe first day= (1+ 2 + 3....+M)units
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Part of the job doneon the second day =(2+ 3 +…+M)units.
Part of the job done on the mlh day = (m +…+ M) units.
And finally, part of the job done on the Mth day = M units
Job =1+2+ 3+ + M
+ 2 + 3 +….+ M
+ 3……….
+ M
= (12 + 22 + 32…..M2) units
= (M)(M + 1)(2M + 1) / 6 units
=>(M)(M + 1)(2M + 1) / 6 = 204 (given)
=> (M) (M + 1) (2M + 1) = 1224 = (8) (9) (17)
comparing both sides, M = 8
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DIRECTIONS for questions: Select the correct alternative from the giv...
Problem Analysis:
Let's assume that there are M workers who started the job. At the end of the ith day, the ith worker leaves the job. The ith worker can do i units of work per day. The total work that needs to be done is 204 units.
We need to find the value of M, i.e., the number of workers who started the job.
Key Points:
- Each worker can do i units of work per day.
- The ith worker leaves the job at the end of the ith day.
- The total work to be done is 204 units.
Solution:
To find the value of M, we need to determine the number of workers who started the job.
Let's analyze the work done by each worker on each day:
- On the 1st day, the 1st worker does 1 unit of work.
- On the 2nd day, the 2nd worker does 2 units of work.
- On the 3rd day, the 3rd worker does 3 units of work.
- ...
- On the ith day, the ith worker does i units of work.
If we sum up the work done by each worker, it will give us the total work done:
1 + 2 + 3 + ... + M = 204
To find the value of M, we need to find the sum of the first M natural numbers.
The sum of the first M natural numbers can be calculated using the formula:
Sum = (M * (M + 1)) / 2
We can solve the equation:
(M * (M + 1)) / 2 = 204
Multiplying both sides by 2:
M * (M + 1) = 408
Expanding the equation:
M^2 + M - 408 = 0
By factoring or using the quadratic formula, we can find the roots of the equation:
(M - 17)(M + 24) = 0
This gives us two possible values for M: M = 17 or M = -24.
Since the number of workers cannot be negative, the only valid solution is M = 17.
Therefore, the correct answer is option A: 17.
Let's assume that there are M workers who started the job. At the end of the ith day, the ith worker leaves the job. The ith worker can do i units of work per day. The total work that needs to be done is 204 units.
We need to find the value of M, i.e., the number of workers who started the job.
Key Points:
- Each worker can do i units of work per day.
- The ith worker leaves the job at the end of the ith day.
- The total work to be done is 204 units.
Solution:
To find the value of M, we need to determine the number of workers who started the job.
Let's analyze the work done by each worker on each day:
- On the 1st day, the 1st worker does 1 unit of work.
- On the 2nd day, the 2nd worker does 2 units of work.
- On the 3rd day, the 3rd worker does 3 units of work.
- ...
- On the ith day, the ith worker does i units of work.
If we sum up the work done by each worker, it will give us the total work done:
1 + 2 + 3 + ... + M = 204
To find the value of M, we need to find the sum of the first M natural numbers.
The sum of the first M natural numbers can be calculated using the formula:
Sum = (M * (M + 1)) / 2
We can solve the equation:
(M * (M + 1)) / 2 = 204
Multiplying both sides by 2:
M * (M + 1) = 408
Expanding the equation:
M^2 + M - 408 = 0
By factoring or using the quadratic formula, we can find the roots of the equation:
(M - 17)(M + 24) = 0
This gives us two possible values for M: M = 17 or M = -24.
Since the number of workers cannot be negative, the only valid solution is M = 17.
Therefore, the correct answer is option A: 17.
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DIRECTIONS for questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. 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 questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. 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 questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. Can you explain this answer?.
DIRECTIONS for questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. 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 questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. 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 questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. Can you explain this answer?.
Solutions for DIRECTIONS for questions: Select the correct alternative from the given choices. M workers started a job. At the end of theith day of the job, where 1 ≤ i ≤ M, the ith worker left the job. The job was completed when the Mth worker left. If the ith worker can do i units of work per day and the job to be done was equal to 204 units of work, find M.a) 8b) 9c) 10d) 7Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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