The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is[2023]Correct answer is '27'. Can you explain this answer?

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The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is

[2023]

Correct answer is '27'. Can you explain this answer?

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The amount of job that Amal, Sunil and Kamal can individually do in a ...

“The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression.” This implies that the amount of time taken individually by Amal, Sunil and Kamal to finish a job are in A.P.
“Kamal takes twice as much time as Amal to do the same amount of job.” Since the amount of time taken individually by Amal, Sunil and Kamal to finish a job are in A.P, this simply means that Sunil Should take 1.5 times the time as Amal to do the same amount of job.
So, to do the same amount of job individually, the times taken by Amal, Sunil and Kamal will be in the ratio, 1 : 1.5 : 2 or 2 : 3 : 4
Amal, Sunil and Kamal worked for 4, 9 and 16 days respectively to finish the job.
Sunil does in 3 days what Amal does in 2 days.
Therefore, Sunil does in 6 days what Amal does in 4 days.
Sunil does in 3 days what Kamal does in 4 days.
Therefore, Sunil does in 12 days what Kamal does in 16 days.
So, to finish the entire job on his own, Sunil would require, 6 + 9 + 12 = 27 days.

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The amount of job that Amal, Sunil and Kamal can individually do in a ...

Given Information:
- Amal, Sunil, and Kamal's individual work rates are in harmonic progression.
- Kamal takes twice as much time as Amal to do the same amount of work.
- Amal works for 4 days, Sunil works for 9 days, and Kamal works for 16 days to finish the job.

Calculating Individual Work Rates:
- Let the individual work rates of Amal, Sunil, and Kamal be 1/A, 1/B, and 1/C respectively.
- According to the given information, the work rates are in harmonic progression. So, 2/B = 1/A + 1/C.

Calculating Kamal's Work Rate:
- Since Kamal takes twice as much time as Amal to do the same amount of work, C = 2A.
- Substituting C = 2A in 2/B = 1/A + 1/C, we get 2/B = 1/A + 1/(2A).
- Simplifying, we get B = 3A.

Calculating Time Taken by Each Person:
- Amal works for 4 days, so his work rate is 4/A.
- Sunil works for 9 days, so his work rate is 9/B = 9/(3A) = 3/A.
- Kamal needs to work for 16 days to finish the remaining job, so his work rate is 16/C = 16/(2A) = 8/A.

Calculating the Remaining Work:
- Total work = Work done by Amal + Work done by Sunil + Work done by Kamal = 4/A + 9/A + 16/A = 29/A.
- Remaining work = Total work - Work done by Amal and Sunil = 29/A - 13/A = 16/A.

Calculating Sunil's Time:
- Sunil's work rate is 3/A, so the time taken by Sunil to finish the remaining work alone is A/3.
- Since A/3 = 27, Sunil will take 27 days to finish the job working alone.

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The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is[2023]Correct answer is '27'. 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 The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is[2023]Correct answer is '27'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is[2023]Correct answer is '27'. Can you explain this answer?.

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