1. **Calculate Worker P's daily work rate:** If P completes the task in 20 days, P completes 1/20 of the task per day. 2. **Calculate Worker Q's daily work rate:** Q is 25% more efficient than P. So, Q's efficiency = P's efficiency × 1.25 = (1/20) × 1.25 = 1.25/20 = 5/80 = 1/16 of the task per day. 3. **Calculate their combined daily work rate:** P + Q = (1/20) + (1/16). The least common multiple (LCM) of 20 and 16 is 80. So, (4/80) + (5/80) = 9/80 of the task per day. 4. **Calculate work done in 5 days:** They worked together for 5 days, so work done = (9/80) × 5 = 45/80 = 9/16 of the task. 5. **Calculate remaining work:** Total work is 1. Remaining work = 1 - (9/16) = 7/16 of the task. 6. **Calculate time Worker P takes to complete remaining work:** Worker P completes 1/20 of the task per day. Time = (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 — Incorrect calculation of remaining work or Worker P's time. B — Arithmetic error in calculating combined efficiency or final division. C — Miscalculation of individual efficiencies or total work completed together. D — (This is the correct answer)

1. Assume the total work is the Least Common Multiple (LCM) of 10, 15, and 30, which is 30 units. 2. Alice's daily work rate (efficiency) = 30 units / 10 days = 3 units/day. 3. Bob's daily work rate = 30 units / 15 days = 2 units/day. 4. Carol's daily work rate = 30 units / 30 days = 1 unit/day. 5. Combined daily work rate of Alice, Bob, and Carol = 3 + 2 + 1 = 6 units/day. 6. Work done in the first 3 days (by A+B+C) = 6 units/day * 3 days = 18 units. 7. Remaining work = Total work - Work done = 30 - 18 = 12 units. 8. Combined daily work rate of Alice and Bob (after Carol leaves) = 3 + 2 = 5 units/day. 9. Additional days required for Alice and Bob to complete the remaining work = Remaining work / (A+B)'s combined daily rate = 12 units / 5 units/day = 2.4 days. Why others are wrong: A — This is the correct calculation. B — Incorrect if the remaining work was miscalculated or an arithmetic error was made in the final division. C — Incorrect; likely represents a misunderstanding of how to calculate remaining work or the combined efficiency. D — Incorrect; suggests a significant error in either the calculation of the remaining work or the combined daily rate of Alice and Bob.

1. Calculate the rate of Machine A: 1/10 of the order per hour. 2. Calculate the rate of Machine B: 1/15 of the order per hour. 3. Calculate their combined rate: (1/10) + (1/15) = 3/30 + 2/30 = 5/30 = 1/6 of the order per hour. 4. Calculate the amount of work completed in the 3 hours they worked together: (1/6) * 3 hours = 1/2 of the order. 5. Determine the remaining work: 1 (total order) - 1/2 (completed) = 1/2 of the order. 6. Calculate the time Machine A needs to complete the remaining work alone: (1/2) / (1/10) = 1/2 * 10 = 5 hours. Why others are wrong: A — This is the correct calculation. B — Incorrectly assumes the remaining work corresponds to half of the total time both machines would take (which is 6 hours for the full order). C — Incorrectly applies Machine B's rate (15 hours for full order) to the remaining half of the work (15 * 0.5 = 7.5 hours). D — Results from miscalculation or an incorrect approach, such as subtracting 3 hours from A's total time and then adding extra time without basis.

Let the total work be the Least Common Multiple (LCM) of 10 and 15, which is 30 units. Liam's daily work rate = 30 units / 10 days = 3 units/day. Sarah's daily work rate = 30 units / 15 days = 2 units/day. Combined daily work rate of Liam and Sarah = 3 units/day + 2 units/day = 5 units/day. Work done by Liam and Sarah together in 4 days = 5 units/day * 4 days = 20 units. Remaining work = Total work - Work done = 30 units - 20 units = 10 units. Time Liam needs to complete the remaining work alone = Remaining work / Liam's daily work rate = 10 units / 3 units/day = 10/3 days = 3 1/3 days. Why others are wrong: B — This would be the time if the remaining work was divided by Sarah's rate (10/2 = 5 days), which is incorrect as Liam finishes the work. C — This represents the total time Liam and Sarah would take to complete the *entire* project if they worked together (30 units / 5 units/day = 6 days), not the additional time Liam takes. D — This would result from various calculation errors, such as miscalculating the remaining work or Liam's rate.

1. Anusha's daily work rate = 1/30 of the project. 2. Bhanu is 25% more efficient than Anusha. Bhanu's efficiency = 1.25 * Anusha's efficiency. 3. Bhanu's daily work rate = 1.25 * (1/30) = (5/4) * (1/30) = 5/120 = 1/24 of the project. 4. Combined daily work rate of Anusha and Bhanu = (1/30) + (1/24) = (4/120) + (5/120) = 9/120 = 3/40 of the project. 5. Work done by Anusha and Bhanu together in 6 days = 6 * (3/40) = 18/40 = 9/20 of the project. 6. Remaining work = Total work - Work done = 1 - (9/20) = 11/20 of the project. 7. Time taken by Bhanu to complete the remaining work = (Remaining Work) / (Bhanu's daily work rate). 8. Time = (11/20) / (1/24) = (11/20) * 24 = 11 * (24/20) = 11 * (6/5) = 66/5 = 13.2 days. Why others are wrong: A — This option is the result of correct calculations. B — This value typically results from miscalculating Bhanu's efficiency or the remaining work fraction. C — This value could arise from errors in determining the combined work rate or the total work completed initially. D — This value often results from a misapplication of the time calculation formula or a miscalculation of the remaining work proportion.