Two persons A and B have work efficiency in the ratio 3: 2 respectively. In how many days can A finish a work alone? I- A and C can together complete a work in 24 days and B and C together can complete 75% of the work in 12 days. II - If B increases his efficiency by 20% then B can finish 20% less work as done by A.

Statement I: A:B efficiency = 3:2. Let A = 3 units/day, B = 2 units/day. A + C: 24 days, so combined rate = 1/24. Let C = c units/day. A + C = 3 + c. B + C: 75% work in 12 days, so rate = 0.75/12 = 1/16. B + C = 2 + c = 1/16, giving c = 1/16 - 2 = -31/16. This gives C = 31/16 units/day. A + C = 3 + 31/16 = 79/16, which matches 1/24 work rate (since 79/16 × 24 = 118.5 ≠ 1). Wait, let me redo. If A + C complete work in 24 days, their combined rate is 1/24 work per day. B + C complete 75% in 12 days, rate = 3/4 × 1/12 = 1/16. With B = 2, C = 1/16 - 2 = -31/16. A + C = 3 + (-31/16) = 17/16. If this completes in 24 days, total work = 24 × 17/16 = 25.5. A alone: 25.5/3 = 8.5 days. Statement I is sufficient. Statement II gives information about B's efficiency but doesn't provide absolute work quantities or time relationships to determine A's individual time. Statement II alone is insufficient.