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, isCorrect 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

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.

Analysis:
- Let the work rates of Amal, Sunil, and Kamal be a, b, and c respectively.
- According to the given information, b = 2a and 1/a + 1/b = 2/b.
- Since 1/a, 1/b, and 1/c are in harmonic progression, we can write 2/b = (2/b) + (1/c).
- Solving these equations, we get a = 1/12, b = 1/6, and c = 1/4.

Calculation:
- Let the total work be represented by LCM(12, 6, 4) = 12.
- Amal can complete 1/12 of the work per day, Sunil can complete 1/6 of the work per day, and Kamal can complete 1/4 of the work per day.
- Amal completes 4 * (1/12) = 1/3 of the work, leaving 2/3 of the work.
- Sunil completes 9 * (1/6) = 3/2 of the work, leaving 1/2 of the work.
- Kamal completes 16 * (1/4) = 4 of the work, finishing the remaining 1/2 of the work.

Final Calculation:
- To find the number of days Sunil will take to finish the remaining 1/2 of the work, we can calculate (1/2) / (1/6) = 3 days.
- Therefore, Sunil will take 3 days to finish the remaining work if 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, isCorrect 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, isCorrect 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, isCorrect answer is '27'. Can you explain this answer?.

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