1. Efficiency and time are inversely proportional when the amount of work is constant (Work = Efficiency × Time). 2. If Mark is 50% more efficient than Sarah, then Mark's efficiency (E_M) can be expressed as 1.5 times Sarah's efficiency (E_S), i.e., E_M = 1.5 × E_S. 3. Since they complete identical tasks, the amount of work (W) is the same for both. So, E_M × T_M = E_S × T_S, where T is time. 4. Substitute E_M: (1.5 × E_S) × T_M = E_S × T_S. 5. Cancel out E_S from both sides: 1.5 × T_M = T_S. 6. Given that Mark's time (T_M) is 6 hours, Sarah's time (T_S) = 1.5 × 6 = 9 hours. Why others are wrong: A — This is the correct answer. B — This would imply Mark is 100% more efficient (twice as fast), not 50%. C — This value does not result from the correct application of the 50% efficiency difference. D — This value does not result from the correct application of the 50% efficiency difference.

1. Efficiency measures the rate at which work is completed relative to the resources used. 2. An increase in efficiency (from 75% to 90%) means the team can accomplish the same amount of work in less time, or more work in the same amount of time. 3. The scenario specifies that the company maintains the *same scope* (amount of work) and *deadlines* for projects. 4. Therefore, if the same amount of work is performed with higher efficiency, the most direct and immediate impact is that the time taken to complete each project will decrease. Why others are wrong: A — This is a potential *consequence* if the company chooses to reduce working hours, not the immediate impact on project completion, and depends on how the saved time is managed. B — While increased efficiency might indirectly allow for more focus on quality, efficiency itself primarily relates to the rate or volume of output, not inherently to an improvement in quality. D — This is a *result* of completing projects faster. The immediate impact on any given project is the reduction in its completion time, which then frees up resources to create greater capacity.

1. Calculate Worker P's daily efficiency: P completes the task in 20 days, so P's daily efficiency is 1/20 of the task. 2. Calculate Worker Q's daily efficiency: Q is 25% more efficient than P. Q's efficiency = P's efficiency + 0.25 * P's efficiency = (1/20) + (1/4 * 1/20) = (1/20) + (1/80) = 4/80 + 1/80 = 5/80 = 1/16 of the task per day. 3. Calculate their combined daily efficiency: (1/20) + (1/16) = (4/80) + (5/80) = 9/80 of the task per day. 4. Calculate work done in the first 5 days by both workers: 5 days * (9/80 task/day) = 45/80 = 9/16 of the task. 5. Calculate the remaining work: Total task = 1. Remaining work = 1 - (9/16) = 7/16 of the task. 6. Calculate the time Worker Q needs to complete the remaining work alone: Time = Remaining Work / Q's daily efficiency = (7/16) / (1/16) = 7 days. Why others are wrong: A — This would imply a faster completion rate for the remaining work, potentially from calculation errors. C — This could result from an incorrect calculation of Q's efficiency or a misstep in determining the remaining work. D — This option could arise if the work done by both workers together was miscalculated or if Q's efficiency was underestimated.

1. Liam's 1-day work rate = 1/20 of the project. 2. Chloe's 1-day work rate = 1/30 of the project. 3. Their combined 1-day work rate = (1/20) + (1/30) = (3 + 2)/60 = 5/60 = 1/12 of the project. 4. Work completed by both in 8 days = 8 * (1/12) = 8/12 = 2/3 of the project. 5. Remaining work = 1 - (2/3) = 1/3 of the project. 6. Time Chloe needs to complete the remaining 1/3 work alone = (1/3) / (1/30) = (1/3) * 30 = 10 days. Why others are wrong: A — This represents the number of days they worked together, not the additional time Chloe needs. B — This is the correct answer. C — This would be the total time if they worked together to complete the entire project, or a miscalculation of Chloe's solo time for remaining work. D — Results from a miscalculation of either the remaining work or Chloe's efficiency.

1. Determine Station X's processing rate: 40 units per hour. 2. Calculate Station Y's processing rate: Y is 25% more efficient than X, so Y's rate = 40 * (1 + 0.25) = 40 * 1.25 = 50 units per hour. 3. Calculate Station Z's processing rate: Z is 10% less efficient than Y, so Z's rate = 50 * (1 - 0.10) = 50 * 0.90 = 45 units per hour. 4. Calculate the combined processing rate of all three stations: 40 (X) + 50 (Y) + 45 (Z) = 135 units per hour. 5. Calculate the total units processed in 2.5 hours: 135 units/hour * 2.5 hours = 337.5 units. 6. Rounding to the nearest whole unit, approximately 338 units can be processed. Why others are wrong: A — Results from an error in calculating individual efficiencies or the combined total. B — Could be an arithmetic error in the combined rate or the multiplication by 2.5 hours. D — Represents an overestimation, possibly from incorrectly calculating Z's efficiency as 10% *more* than Y, or other miscalculations.