1. Let Ben's efficiency be 1 unit of work per day. 2. Anya is 50% more efficient than Ben, so Anya's efficiency is 1 + 0.50 = 1.5 units of work per day. 3. Their combined efficiency is 1 (Ben) + 1.5 (Anya) = 2.5 units of work per day. 4. They work together for 6 days, completing 2.5 units/day * 6 days = 15 units of work. 5. The remaining 25% of the project is completed by Anya alone. This means the 15 units of work they did together constitutes 100% - 25% = 75% of the total project. 6. To find the total work, we set up the equation: 0.75 * Total Work = 15 units. 7. Total Work = 15 / 0.75 = 20 units. 8. The question asks how many days Ben would take to complete the entire project alone. Ben's efficiency is 1 unit/day. 9. Time for Ben alone = Total Work / Ben's Efficiency = 20 units / 1 unit/day = 20 days. Why others are wrong: A — This represents the amount of work completed together, not the total project size for Ben to complete alone. B — This option does not follow a common miscalculation path based on the given information. D — This would be the answer if Anya was *twice* as efficient as Ben (instead of 50% more), making their combined efficiency 3 units/day, completing 18 units in 6 days, which would then be 75% of a 24-unit project.

1. Calculate individual repair rates: Sarah's rate = 30 devices / 6 hours = 5 devices/hour. Tom's rate = 30 devices / 10 hours = 3 devices/hour. 2. Calculate their combined repair rate when working together: Combined rate = 5 devices/hour + 3 devices/hour = 8 devices/hour. 3. Calculate the number of devices repaired in the first 2 hours by both: Devices repaired = 8 devices/hour * 2 hours = 16 devices. 4. Calculate the number of devices remaining: Remaining devices = 60 devices - 16 devices = 44 devices. 5. Calculate the time Tom takes to repair the remaining devices alone: Time for Tom = 44 devices / 3 devices/hour = 44/3 hours. 6. Calculate the total time taken: Total time = 2 hours (both working) + 44/3 hours (Tom alone) = 6/3 hours + 44/3 hours = 50/3 hours = 16 and 2/3 hours. Why others are wrong: A — Results from an incorrect calculation of either the combined work or Tom's remaining time. B — Likely results from rounding or a miscalculation of the fractional part of Tom's remaining time. D — Suggests an overestimation, possibly by miscalculating one of the segments of work or rates.

1. **Calculate individual efficiencies:** * Alex's efficiency = 1/20 project/day. * Ben's efficiency = Alex's efficiency * (1 + 0.25) = (1/20) * 1.25 = 1/16 project/day (since Ben completes the project in 20/1.25 = 16 days). * Chris's efficiency = 1/30 project/day. 2. **Calculate work done by Alex and Ben together:** * Combined efficiency (Alex + Ben) = 1/20 + 1/16 = (4+5)/80 = 9/80 project/day. * Work done in 4 days = 4 * (9/80) = 36/80 = 9/20 of the project. 3. **Calculate remaining work:** * Remaining work = 1 - 9/20 = 11/20 of the project. 4. **Calculate combined efficiency of Ben and Chris:** * Combined efficiency (Ben + Chris) = 1/16 + 1/30. * Find LCM of 16 and 30, which is 240. * (15/240) + (8/240) = 23/240 project/day. 5. **Calculate time to finish remaining work:** * Time = Remaining work / Combined efficiency (Ben + Chris) * Time = (11/20) / (23/240) = (11/20) * (240/23) * Time = (11 * 12) / 23 (since 240/20 = 12) * Time = 132/23 days. * 132 divided by 23 is 5 with a remainder of 17, so 5 17/23 days. Why others are wrong: A — Correct calculation. B — Likely results from an arithmetic error in calculating combined efficiency or remaining work. C — Likely results from an arithmetic error in calculating combined efficiency or remaining work. D — This represents the total time taken for the entire project (4 days + 5 17/23 days), not just the remaining work.

1. Assume the total work is the Least Common Multiple (LCM) of 12 and 18, which is 36 units. 2. Amara's efficiency = Total work / Days Amara takes = 36 units / 12 days = 3 units/day. 3. Ben's efficiency = Total work / Days Ben takes = 36 units / 18 days = 2 units/day. 4. Combined efficiency of Amara and Ben = Amara's efficiency + Ben's efficiency = 3 + 2 = 5 units/day. 5. Work done in the first 3 days (by Amara and Ben together) = Combined efficiency × Days worked = 5 units/day × 3 days = 15 units. 6. Remaining work = Total work - Work done = 36 units - 15 units = 21 units. 7. Time Amara needs to complete the remaining work = Remaining work / Amara's efficiency = 21 units / 3 units/day = 7 days. Why others are wrong: A — Incorrect calculation of remaining work (e.g., assuming 18 units remaining) or Amara's efficiency. B — (Correct Answer) C — Possible if work done together was miscalculated, leading to a remaining work of 24 units. D — Could be a result of a significant error in the work done or remaining work calculation.

1. Assume the total work is 1 unit. Alon's daily work rate = 1/30. 2. Ben's efficiency is 20% more than Alon's. Ben's daily work rate = 1.20 * (1/30) = 1.2/30 = 1/25. 3. Combined daily work rate of Alon and Ben = (1/30) + (1/25) = (5 + 6)/150 = 11/150. 4. Work done by Alon and Ben in 5 days = 5 * (11/150) = 11/30. 5. Remaining work = 1 - (11/30) = 19/30. 6. Chloe's efficiency is 10% less than Ben's. Chloe's daily work rate = 0.90 * (1/25) = 9/250. 7. Combined daily work rate of Ben and Chloe = (1/25) + (9/250) = (10/250) + (9/250) = 19/250. 8. Time taken by Ben and Chloe to complete the remaining work = (Remaining Work) / (Combined daily work rate of Ben and Chloe) = (19/30) / (19/250) = (19/30) * (250/19) = 250/30 = 25/3 days. 9. 25/3 days = 8 1/3 days. Why others are wrong: A — Incorrect calculation of remaining work or combined efficiency for the second phase. B — Likely results from rounding intermediate steps or an arithmetic error. D — Error in calculating efficiency percentages or the initial work completed.