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:
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:
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:
Options
Answer: (2) 21
Explanation:
Step 1: Express R + G in terms of K 6(R + G) + 9K = 1 → R + G = (1 − 9K)/6 Step 2: Use inequalities R + G > 1/15 → (1 − 9K)/6 > 1/15 → 9K < 0.6 → K < 0.0667 R + K + G < 1/7 → (R + G) + K < 1/7 → (1 − 9K)/6 + K < 1/7 → 3K > 1/7 → K > 0.0476 Step 3: Range for K K ∈ (1/21, 1/15) ≈ (0.0476, 0.0667) Number of days Rakshita alone would take = 1/K ∈ (15, 21) Step 4: Conclusion Rakshita alone cannot take less than 15 days or more than 21 days. Answer: Number of days Rakshita alone would take cannot be ≤ 15 or ≥ 21
Explanation:
Step 1: Express R + G in terms of K 6(R + G) + 9K = 1 → R + G = (1 − 9K)/6 Step 2: Use inequalities R + G > 1/15 → (1 − 9K)/6 > 1/15 → 9K < 0.6 → K < 0.0667 R + K + G < 1/7 → (R + G) + K < 1/7 → (1 − 9K)/6 + K < 1/7 → 3K > 1/7 → K > 0.0476 Step 3: Range for K K ∈ (1/21, 1/15) ≈ (0.0476, 0.0667) Number of days Rakshita alone would take = 1/K ∈ (15, 21) Step 4: Conclusion Rakshita alone cannot take less than 15 days or more than 21 days. Answer: Number of days Rakshita alone would take cannot be ≤ 15 or ≥ 21
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