1. Let the individual rates of P, Q, and R be 1/P, 1/Q, and 1/R assemblies per hour, respectively. 2. From the given information, we can form three equations: * 1/P + 1/Q = 1/12 (P and Q together complete 1/12 of the work per hour) * 1/Q + 1/R = 1/15 (Q and R together complete 1/15 of the work per hour) * 1/P + 1/R = 1/20 (P and R together complete 1/20 of the work per hour) 3. Add all three equations: * (1/P + 1/Q) + (1/Q + 1/R) + (1/P + 1/R) = 1/12 + 1/15 + 1/20 * 2(1/P + 1/Q + 1/R) = 1/12 + 1/15 + 1/20 4. Find a common denominator for the right side, which is 60: * 2(1/P + 1/Q + 1/R) = 5/60 + 4/60 + 3/60 * 2(1/P + 1/Q + 1/R) = 12/60 * 2(1/P + 1/Q + 1/R) = 1/5 5. To find the combined rate of P, Q, and R (1/P + 1/Q + 1/R), divide by 2: * 1/P + 1/Q + 1/R = (1/5) / 2 * 1/P + 1/Q + 1/R = 1/10 6. This combined rate means they complete 1/10 of the assembly per hour. Therefore, the total time to complete one assembly is the reciprocal of this rate. * Time = 10 hours. Why others are wrong: A — Correct. B — This would be the result if one calculated the sum of the rates (1/12 + 1/15 + 1/20 = 1/5) and then incorrectly took its reciprocal without dividing by 2, effectively calculating for two sets of P, Q, and R. C — This might arise from incorrectly averaging the given times, or misinterpreting the combined efficiency if all three worked together. D — This option represents an arbitrary incorrect calculation or an estimation that doesn't follow the principles of efficiency and time.

1. Determine Worker P's daily work rate: P completes 1/20 of the project per day. 2. Determine Worker Q's efficiency: Q is 25% more efficient than P, so Q's efficiency factor is 1 + 0.25 = 1.25. 3. Determine Worker Q's daily work rate: Q's rate = 1.25 * (1/20) = 5/4 * (1/20) = 5/80 = 1/16 of the project per day. 4. Calculate the combined daily work rate of P and Q: (1/20) + (1/16). Find a common denominator, which is 80: (4/80) + (5/80) = 9/80 of the project per day. 5. Calculate the work done by P and Q together in the first 4 days: 4 days * (9/80 project/day) = 36/80 = 9/20 of the project. 6. Calculate the remaining work: Total work (1) - Work done (9/20) = 1 - 9/20 = 11/20 of the project. 7. Calculate the time Worker Q will take to complete the remaining work alone: Remaining work / Q's daily work rate = (11/20) / (1/16) = (11/20) * 16 = 176/20 = 44/5 = 8.8 days. Why others are wrong: A — Correct calculation. B — Likely a result of a minor calculation error or incorrect rounding of an intermediate step. C — Could result from miscalculating Q's efficiency or an error in calculating the remaining work. D — Suggests a significant miscalculation in either individual work rates or the work completed together.

1. Architect A's daily work rate is 1/24 of the project. 2. Architect B's daily work rate is 1/36 of the project. 3. When working together, their combined daily rate is (1/24) + (1/36) = (3/72) + (2/72) = 5/72 of the project per day. 4. In the first 9 days, the work completed by both architects together is 9 * (5/72) = 45/72 = 5/8 of the project. 5. The remaining portion of the project is 1 - 5/8 = 3/8. 6. Architect A needs to complete this remaining 3/8 of the project alone. 7. Time taken by A to complete 3/8 of the project = (3/8) / (1/24) = (3/8) * 24 = 3 * 3 = 9 days. Why others are wrong: A — Incorrectly calculates remaining work or applies the wrong efficiency for the remaining task. B — Likely results from an error in calculating the remaining work fraction or A's daily contribution. D — This is the total time A and B would take to complete the *entire* project together (1 / (5/72) = 14.4 days), or possibly miscalculating A's remaining time based on a different fraction.

1. Anika's one-day work rate = 1/20 of the project. 2. Bilal's one-day work rate = 1/30 of the project. 3. Their combined one-day work rate = (1/20) + (1/30) = (3+2)/60 = 5/60 = 1/12 of the project. 4. Work completed in 6 days by Anika and Bilal together = 6 * (1/12) = 1/2 of the project. 5. Remaining work = 1 (total work) - 1/2 (work done) = 1/2 of the project. 6. Time taken by Anika to complete the remaining 1/2 work = (Remaining Work) / (Anika's one-day work rate) = (1/2) / (1/20) = 1/2 * 20 = 10 days. Why others are wrong: A — This option might arise from miscalculating the combined work or remaining portion. C — This is the total time it would take for both Anika and Bilal to complete the *entire* project if they worked together, not the additional days for Anika alone. D — This option incorrectly assumes that Anika's remaining work time is simply her total individual time minus the days already worked, ignoring Bilal's contribution during those initial 6 days.

1. Calculate individual daily efficiencies: Worker P's daily efficiency = 1/15 of the project. Worker Q's daily efficiency = 1/20 of the project. 2. Calculate combined daily efficiency when working together: Combined efficiency = (1/15) + (1/20) = (4/60) + (3/60) = 7/60 of the project per day. 3. Calculate the portion of work completed in the initial 4 days: Work completed = 4 days * (7/60 project/day) = 28/60 = 7/15 of the project. 4. Calculate the remaining portion of the project: Remaining work = 1 - (7/15) = 8/15 of the project. 5. Calculate the time Worker Q needs to complete the remaining work alone: Time = Remaining Work / Worker Q's daily efficiency Time = (8/15) / (1/20) = (8/15) * 20 = 160/15 = 32/3 days. 32/3 days can be expressed as 10 and 2/3 days. Why others are wrong: A — This is the correct calculation based on the daily efficiencies and remaining work. B — Incorrect calculation, possibly from an error in finding the combined rate or the remaining work fraction. C — Incorrect calculation, likely from miscalculating the remaining work (e.g., assuming it was 1/2 of the project). D — Incorrect calculation, likely due to a minor arithmetic error in calculating the remaining work or the final division.