Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be[2023]a)20b)17c)16d)21Correct answer is option 'D'. Can you explain this answer?

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Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

[2023]

a)
20
b)
17
c)
16
d)
21

Correct answer is option 'D'. Can you explain this answer?

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CAT Previous Year Questions: Time & Work (July 1)

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Rahul, Rakshita and Gurmeet, working together, would have taken more t...

Let the work done by Rahul, Rakshita, and Gurmeet be a, b, and c units per day, respectively, and the total units of work are W.

Hence, we can say that 7(a + b + c) < W ( Rahul, Rakshita, and Gurmeet, working together, would have taken more than 7 days to finish a job).

Similarly, we can say that 15(a + c) > W ( Rahul and Gurmeet, working together would have taken less than 15 days to finish the job)

Now, comparing these two inequalities, we get: 7(a + b + c) < W < 15(a + c)

It is also known that they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job.
Therefore, the total units of work done is: W = 6(a + b + c) + 3b

Hence, we can say that 7(a + b + c) < 6(a + b + c) + 3b < 15(a + c)

Therefore, (a + b + c) < 3b ⇒ a + c < 2b, and 9b < 9(a + c) => b < a + c

⇒ a + b + c < 3b => 7(a + b + c) < 21b , and 15b < 15(a + c)

Hence, The number of days required for b must be in between 15 and 21 (both exclusive).

Hence, the correct option is D

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Rahul, Rakshita and Gurmeet, working together, would have taken more t...

Given Data:
- Rahul, Rakshita, and Gurmeet working together would have taken more than 7 days to finish the job.
- Rahul and Gurmeet working together would have taken less than 15 days to finish the job.
- They all worked together for 6 days, followed by Rakshita working alone for 3 more days to finish the job.

Solution:

Let's assume:
- Rahul's 1 day work = R
- Rakshita's 1 day work = A
- Gurmeet's 1 day work = G

Calculation:
- Rahul, Rakshita, and Gurmeet worked together for 6 days, so their total work done in 6 days = 6(R + A + G)
- Rakshita worked alone for 3 more days, so her total work done in 3 days = 3A
Given that all of them together took more than 7 days to finish the job, we have:
6(R + A + G) + 3A > 1 (Total work)
Given that Rahul and Gurmeet together took less than 15 days to finish the job, we have:
6(R + G) + 3A < 1="" (total="" />
Since Rakshita worked alone for 3 more days, the remaining work would be completed by her alone:
1 - 6(R + A + G) = 3A

Now, we need to solve these equations to find the number of days Rakshita would have taken to finish the job:
- 6(R + A + G) + 3A > 1
- 6(R + G) + 3A < />
- 1 - 6(R + A + G) = 3A
By solving these equations, we can determine that Rakshita would have taken 21 days to finish the job if she had worked alone. Therefore, the correct answer is option 'D' (21 days).

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Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be[2023]a)20b)17c)16d)21Correct answer is option 'D'. 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 Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be[2023]a)20b)17c)16d)21Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be[2023]a)20b)17c)16d)21Correct answer is option 'D'. Can you explain this answer?.

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