Discussion

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

Explanation:

Let the total work to be done = LCM(7, 15, 6) = 630 units.

⇒ Combined efficiency of Rahul, Rakshita and Gurmeet < 630/7 = 90 units/day

All 3 worked for 6 days and then Rakshita worked for 3 days. Calculating total work done
∴ 630 = (combined efficiency of all 3) × 6 + (efficiency of Rakshita) × 3
⇒ (efficiency of Rakshita) × 3 = 630 - (combined efficiency of all 3) × 6
⇒ (efficiency of Rakshita) = 210 - (combined efficiency of all 3) × 2
⇒ (efficiency of Rakshita) > 210 - 90 × 2
⇒ (efficiency of Rakshita) > 30

∴ Rakshita's efficiency is greater than 30 units/day.

⇒ Time taken by Rakshita < 630/30 = 21 days.

∴ Rakshita will take less than 21 days to finish the job. Hence, she cannot take 21 days to finish the job.

Hence, option (a).

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