Question:

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

Updated On: Sep 17, 2024
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  • 21
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  • 20
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The Correct Option is B

Solution and Explanation

Let a, b, and c be the daily work units completed by Rahul, Rakshita, and Gurmeet, respectively. The total work units would be W.
Therefore, we can conclude that \(7(a+b+c) < W\) (because Rahul, Rakshita, and Gurmeet would have needed more than 7 days to complete a task if they had worked together).
Similar to this, we can state that \(15(a+c) > W\), meaning that Rahul and Gurmeet could have completed the task in less than 15 days if they had collaborated.
Now, when we contrast these two inequalities, we obtain: \(15(a+c) < W < 7(a+b+c) \)
It is also reported that Rakshita worked alone for three more days to complete the task after they had all collaborated for six days. \(W = 6(a+b+c)+3b\) represents the total amount of work completed.
Thus, we can state that \(6(a+b+c)+3b < 15(a+c) = 7(a+b+c).\)
\(A+b+c < 3b\)
\(⇒ 7(a+b+c) < 21b,\) and \(15b < 15(a+c) \) imply that \((a+b+c) < 3b\)
 \(⇒ a+c < 2b\) and \(9b < 9(a+c)\)
\( ⇒ b < a+c.\)
Therefore, the days needed for B must fall between 15 and 21 (inclusive).
Therefore, choice B is the right one. 

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