CAT 2023 Slot 3 Solved Paper

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, $(a+b+c) < 3b \Rightarrow a+c < 2b$, and $9b < 9(a+c) \Rightarrow b < a+c$$\Rightarrow a+b+c < 3b \Rightarrow 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