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

• A. 16
• B. 21
• C. 17
• D. 20

Answer 1

Answer: (B)

21

Answer 2

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.