1. Ama's daily work rate = 1/20 of the project. 2. Ben is 25% more efficient than Ama, so Ben's daily work rate = 1.25 * (1/20) = 5/4 * (1/20) = 1/16 of the project. 3. Their combined daily work rate = (1/20) + (1/16) = (4/80) + (5/80) = 9/80 of the project. 4. Work done by Ama and Ben together in 8 days = 8 * (9/80) = 72/80 = 9/10 of the project. 5. Remaining work = 1 - (9/10) = 1/10 of the project. 6. Time taken by Ama to complete the remaining 1/10 work = (1/10) / (1/20) = 2 days. Why others are wrong: A — Correct answer based on calculations. B — Results from miscalculation of the remaining work or Ama's finishing time. C — Occurs if Ben's efficiency or the combined work rate is miscalculated. D — Could be a result of an incorrect interpretation of work remaining or Ama's rate.

1. **Calculate individual efficiencies:** * Anya's efficiency: 1/20 report per hour. * Ben's efficiency: Ben is 25% more efficient than Anya, so his efficiency is (1/20) * 1.25 = 1/16 report per hour. (Ben completes the report in 20 / 1.25 = 16 hours). * Chloe's efficiency: Chloe is 50% less efficient than Ben, so her efficiency is (1/16) * (1 - 0.50) = (1/16) * 0.50 = 1/32 report per hour. (Chloe completes the report in 16 / 0.50 = 32 hours). 2. **Calculate work done by Anya and Chloe in the first 5 hours:** * Combined efficiency of Anya and Chloe = 1/20 + 1/32 = 8/160 + 5/160 = 13/160 report per hour. * Work done in 5 hours = (13/160) * 5 = 65/160 = 13/32 of the report. 3. **Determine the remaining work:** * Remaining work = 1 - 13/32 = 19/32 of the report. 4. **Calculate the combined efficiency of Anya, Ben, and Chloe:** * Combined efficiency (Anya + Ben + Chloe) = 1/20 + 1/16 + 1/32 = 8/160 + 10/160 + 5/160 = 23/160 report per hour. 5. **Calculate the time needed to complete the remaining work:** * Time = Remaining Work / Combined Efficiency = (19/32) / (23/160) = (19/32) * (160/23) = 19 * (160/32) / 23 = 19 * 5 / 23 = 95/23 hours. Why others are wrong: A — This is the correct calculation. B — This could result from an error in calculating the initial work done, for instance, if only 12/32 of the report was completed, or miscalculation of combined efficiency. C — This could result from an error in calculating Chloe's efficiency (e.g., if 50% less efficient was interpreted as 50% of Anya's efficiency, or other miscalculations). D — This could result from various miscalculations in individual efficiencies or the initial work completed before Ben joined.

1. **Calculate individual daily work rates:** * A's daily work rate = 1/20 of the project. * B's efficiency is 25% more than A. So, B's daily work rate = (1/20) * (1 + 0.25) = (1/20) * 1.25 = (1/20) * (5/4) = 5/80 = 1/16 of the project. * C's daily work rate = 1/30 of the project. 2. **Calculate combined daily work rate of A, B, and C:** * (1/20) + (1/16) + (1/30) * Find a common denominator (LCM of 20, 16, 30 is 240): * (12/240) + (15/240) + (8/240) = (12 + 15 + 8)/240 = 35/240 = 7/48 of the project per day. 3. **Calculate work done in the first 5 days (by A, B, and C):** * (7/48) * 5 = 35/48 of the project. 4. **Calculate the remaining work:** * 1 - (35/48) = 13/48 of the project. 5. **Calculate combined daily work rate of B and C (after A leaves):** * (1/16) + (1/30) * Find a common denominator (LCM of 16, 30 is 240): * (15/240) + (8/240) = 23/240 of the project per day. 6. **Calculate additional days for B and C to finish remaining work:** * Remaining work / (B + C's combined rate) = (13/48) / (23/240) * (13/48) * (240/23) = 13 * (240/48) / 23 = 13 * 5 / 23 = 65/23 days. Why others are wrong: A — This is the correct calculation. B — This result (2.5 days) would be obtained if B was mistakenly assumed to be 25% *less efficient* (taking 25% *more* time than A, so 20 * 1.25 = 25 days, for a rate of 1/25). C — This result (13/3 days) would be obtained if only Person B (at a rate of 1/16) was assumed to complete the remaining work of 13/48, ignoring Person C's contribution. (13/48) / (1/16) = (13/48) * 16 = 13/3. D — This result (115/22 days) would be obtained if B was mistakenly assumed to take 25% *more* time than A (i.e., B takes 25 days to complete the task), leading to incorrect combined work rates.

Let the total work be 1 unit. Anuj's daily work rate = 1/20 units/day. Bhavya is 25% more efficient than Anuj, so Bhavya's efficiency factor = 1 + 0.25 = 1.25. Bhavya's daily work rate = 1.25 * (1/20) = (5/4) * (1/20) = 1/16 units/day. Combined daily work rate of Anuj and Bhavya = (1/20) + (1/16) = (4/80) + (5/80) = 9/80 units/day. Work done by Anuj and Bhavya together in 4 days = 4 * (9/80) = 36/80 = 9/20 units. Remaining work = 1 - (9/20) = 11/20 units. Time taken by Bhavya to complete the remaining work = (Remaining work) / (Bhavya's daily work rate) = (11/20) / (1/16) = (11/20) * 16 = 11 * (16/20) = 11 * (4/5) = 44/5 = 8.8 days. Why others are wrong: A — Correct calculation. B — This would be the time taken if Anuj alone completed the remaining 11/20 of the work (11/20 divided by 1/20 = 11 days). C — This represents the total time to complete the project (4 days of combined work + 8.8 days of Bhavya's solo work = 12.8 days), not just the additional days Bhavya takes. D — This result could occur if Bhavya's individual work time was incorrectly estimated as 15 days (e.g., 20 - 25% of 20 = 15 days, instead of 20 / 1.25 = 16 days) leading to an incorrect daily rate of 1/15, and subsequent calculation errors for the remaining work.

1. Worker P's daily work rate is 1/20 of the task. 2. Worker Q's efficiency is 25% more than P's. So, Q's daily work rate = (1/20) * 1.25 = (1/20) * (5/4) = 5/80 = 1/16 of the task. 3. Combined daily work rate of P and Q = (1/20) + (1/16) = (4/80) + (5/80) = 9/80 of the task. 4. Work completed by P and Q together in 5 days = (9/80) * 5 = 45/80 = 9/16 of the task. 5. Remaining work = 1 - (9/16) = 7/16 of the task. 6. Time taken by Worker P to complete the remaining 7/16 of the task alone = (Remaining Work) / (P's daily work rate) = (7/16) / (1/20) = (7/16) * 20 = 140/16 = 35/4 = 8.75 days. Why others are wrong: A — Correct answer derived from accurate calculation of efficiencies and work completed. B — Incorrect calculation of remaining work or misapplication of Worker P's rate. C — Likely assumes both workers have the same efficiency, leading to a miscalculation of combined work and remaining task. D — Error in calculating the time Worker P needs, possibly using an incorrect remaining work portion or efficiency.