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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)
    17
  • b)
    21
  • c)
    16
  • d)
    20
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
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).
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Community Answer
Rahul, Rakshita and Gurmeet, working together, would have taken more t...
Given Information:
- 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.

Calculations:
Let's assume:
- Rahul's 1 day's work = R
- Rakshita's 1 day's work = A
- Gurmeet's 1 day's work = G
Now, we can form the equations based on the given information:
1. (R + A + G) * 6 = Job completed in 6 days
2. (R + G) * 6 + A * 3 = Job completed in 9 days
From equation 1 and 2:
6R + 6A + 6G = 1
6R + 6G + 3A = 1
Solving the equations:
3A = 0
A = 0
Therefore, Rakshita's 1 day's work is 0, which means she will not be able to finish the job alone. Since Rakshita's work is 0, the number of days she would take to finish the job alone is undefined, making option B (21 days) the correct 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)17b)21c)16d)20Correct answer is option 'B'. Can you explain this answer?
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