Which information is/are necessary to answer the questions asked? Two persons A and B have work efficiency in the ratio 1: 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 80% 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.

A and B have efficiency ratio 1:2. Let A's rate = a, B's rate = 2a. Statement I: A + C together take 24 days, so their combined rate is 1/24. B + C together complete 80% in 12 days, so their combined rate is 0.8/12 = 1/15. We have: a + c = 1/24 and 2a + c = 1/15. Subtracting: a = 1/15 - 1/24 = (8-5)/120 = 3/120 = 1/40. So A takes 40 days alone. Statement I alone is sufficient. Statement II: If B's efficiency increases by 20%, new rate is 2.4a. B finishes 20% less work than A. This doesn't give us absolute values or time to complete specific work. Not sufficient.