A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

Step 1: Normalize the capabilities (Unitary Method)\nAs seen in the 2016 question [48], we first need the time for the full job.\n- Person X: 20% work takes 8 days. So, 100% work (which is 5 times more) takes 8 x 5 = 40 days.\n- Person Y: 25% work takes 6 days. So, 100% work (which is 4 times more) takes 6 x 4 = 24 days.\n\nStep 2: Define Total Work (LCM Method)\nInstead of fractions, we assume Total Work is a number easy to divide by 40 and 24. A good number is 120 units (LCM). This is the standard efficiency method used in 2015 [61, 63].\n\nStep 3: Calculate Speeds (Efficiency)\n- X's speed = 120 units / 40 days = 3 units/day.\n- Y's speed = 120 units / 24 days = 5 units/day.\n\nStep 4: Combine and Solve\nWhen working together, speeds add up [31, 71].\n- Combined Speed = 3 + 5 = 8 units/day.\n\nThe question asks for time to do 40% of the work.\n- Target Work = 40% of 120 units = 48 units.\n\n- Time Needed = Target Work / Combined Speed\n- Time = 48 units / 8 units/day = 6 days.