1. **Calculate combined daily work rate**: A and B together complete the project in 12 days, so their combined daily work rate is 1/12 of the project. 2. **Calculate A's daily work rate**: A alone completes the project in 18 days, so A's daily work rate is 1/18 of the project. 3. **Calculate B's original daily work rate**: B's daily work rate = (Combined daily work rate) - (A's daily work rate) = 1/12 - 1/18 = (3 - 2)/36 = 1/36 of the project. This means B alone would take 36 days to complete the project. 4. **Calculate work done in 4 days**: A and B work together for 4 days. Work done = 4 * (1/12) = 4/12 = 1/3 of the project. 5. **Calculate remaining work**: Remaining work = Total work - Work done = 1 - 1/3 = 2/3 of the project. 6. **Calculate B's required daily work rate**: B needs to complete the remaining 2/3 of the project in 15 days. So, B's required daily work rate = (2/3) / 15 = 2/45 of the project. 7. **Calculate percentage increase in efficiency**: Original efficiency (B's daily work rate) = 1/36. Required efficiency (B's daily work rate) = 2/45. To find the percentage increase, use the formula: ((Required Efficiency / Original Efficiency) - 1) * 100% = ((2/45) / (1/36) - 1) * 100% = ((2/45) * 36 - 1) * 100% = (72/45 - 1) * 100% = (8/5 - 1) * 100% = (1.6 - 1) * 100% = 0.6 * 100% = 60%. Why others are wrong: A — This percentage would result from an error in calculating the remaining work or the required daily rate. B — Likely results from a miscalculation of B's original efficiency or an incorrect application of the percentage increase formula. D — Suggests a significant error in determining B's required work rate or comparing it to the original efficiency.

1. The total work required is 120 standard man-hours. 2. Each worker operates at 60% of standard efficiency. 3. Initial team efficiency (5 workers) = 5 workers * 0.6 (efficiency per worker) = 3 units of standard work per hour. 4. Work completed in the first 8 hours = 3 units/hour * 8 hours = 24 standard man-hours. 5. Remaining work = 120 standard man-hours - 24 standard man-hours = 96 standard man-hours. 6. After reassignment, the new team size is 5 - 2 = 3 workers. 7. New team efficiency (3 workers) = 3 workers * 0.6 (efficiency per worker) = 1.8 units of standard work per hour. 8. Additional time needed to complete the remaining work = Remaining work / New team efficiency. 9. Additional time = 96 man-hours / 1.8 man-hours/hour = 960 / 18 hours = 160 / 3 hours. 10. 160 / 3 hours = 53 and 1/3 hours, which is 53 hours and 20 minutes. Why others are wrong: A — This option might result from an incorrect calculation of remaining work or misapplication of efficiency. B — This option is likely a result of an arithmetic error in calculating the remaining time. D — This option indicates an overestimation of the remaining time needed, possibly due to an incorrect remaining work or team efficiency calculation.

1. Calculate the experienced technician's assembly rate: 6 gadgets/hour. 2. Calculate the trainee technician's efficiency: 60% of 6 gadgets/hour = 0.60 * 6 = 3.6 gadgets/hour. 3. Calculate their combined assembly rate per hour: 6 gadgets/hour (experienced) + 3.6 gadgets/hour (trainee) = 9.6 gadgets/hour. 4. Calculate their combined work output per day (working 8 hours): 9.6 gadgets/hour * 8 hours/day = 76.8 gadgets/day. 5. Calculate the total number of days needed to assemble 192 gadgets: 192 gadgets / 76.8 gadgets/day = 2.5 days. Why others are wrong: A — This is the correct calculation. B — This could result from various miscalculations, such as slightly underestimating combined daily output. For example, if the combined daily output was mistakenly calculated as 64 gadgets/day (192/64 = 3). C — This would be the time taken if only the experienced technician worked (192 gadgets / (6 gadgets/hour * 8 hours/day) = 192 / 48 = 4 days). D — This could result from incorrectly averaging their individual hourly rates ((6 + 3.6)/2 = 4.8 gadgets/hour) and then calculating based on that (192 / (4.8 * 8) = 192 / 38.4 = 5 days).

1. Alex's daily work rate is 1/20 of the project. 2. Ben is 25% more efficient than Alex, so Ben's daily work rate is (1/20) * 1.25 = (1/20) * (5/4) = 5/80 = 1/16 of the project. 3. Their combined daily work rate is (1/20) + (1/16) = (4/80) + (5/80) = 9/80 of the project. 4. In 4 days, the work completed by both of them is (9/80) * 4 = 36/80 = 9/20 of the project. 5. The remaining work is 1 - (9/20) = 11/20 of the project. 6. Ben alone will complete the remaining work at his rate of 1/16 per day. 7. Time taken by Ben = (Remaining work) / (Ben's daily work rate) = (11/20) / (1/16) = (11/20) * 16 = 11 * (4/5) = 44/5 = 8.8 days. Why others are wrong: A — Incorrect calculation of Ben's efficiency or remaining work, possibly leading to 15/2 of 1/4 (e.g., if Ben's efficiency was miscalculated or remaining work was wrong). B — May result from rounding or an error in calculating the remaining work or Ben's rate. For instance, if the remaining work was mistakenly calculated as 1/2, or if Ben's rate was incorrectly taken as 1/11. C — This is the correct calculation. D — Likely an arithmetic error in the final step or a miscalculation of combined work rate.

1. Determine Artisan X's hourly work rate: X completes 1 carving in 18 hours, so X's rate is 1/18 of a carving per hour. 2. Determine Artisan Y's time to complete one carving: Y is 20% less efficient than X, meaning Y's efficiency is 80% (or 0.8) of X's. Therefore, Y will take 1 / 0.80 = 1.25 times longer than X. 3. Calculate Y's time to complete one carving: Y's time = 18 hours * 1.25 = 22.5 hours. 4. Determine Artisan Y's hourly work rate: Y completes 1 carving in 22.5 hours, so Y's rate is 1/22.5, which simplifies to 2/45 of a carving per hour. 5. Calculate their combined hourly work rate: Combined rate = X's rate + Y's rate = 1/18 + 2/45. 6. Find a common denominator for 18 and 45, which is 90: 1/18 becomes 5/90; 2/45 becomes 4/90. 7. Combined rate = 5/90 + 4/90 = 9/90 = 1/10 of a carving per hour. 8. Calculate the total time to complete one carving together: Time = 1 / (Combined rate) = 1 / (1/10) = 10 hours. Why others are wrong: A — Incorrect calculation, possibly if Y's efficiency was higher or an error in combining rates. B — Incorrect calculation, likely an error in interpreting "20% less efficient" or in finding the common work rate. C — Correct answer. D — Incorrect calculation, possibly by averaging their individual times or other common mathematical errors in inverse proportionality.