X can do a piece of work in 4 days and Y can do the same piece of work in 6 days. Which of the following statements is/are correct? I. If X and Y work alternately starting with X, then the piece of work will be finished on the fifth day. II. If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.

X does 1/4 per day, Y does 1/6 per day. Starting with X: Day 1 (X): 1/4. Day 2 (Y): 1/4+1/6 = 5/12. Day 3 (X): 5/12+1/4 = 8/12 = 2/3. Day 4 (Y): 2/3+1/6 = 5/6. Day 5: remaining 1/6, X does 1/4 per day, so 1/6 ÷ 1/4 = 2/3 of day 5. Finished on day 5. I is correct. Starting with Y: Day 1 (Y): 1/6. Day 2 (X): 1/6+1/4 = 5/12. Day 3 (Y): 5/12+1/6 = 7/12. Day 4 (X): 7/12+1/4 = 10/12 = 5/6. Day 5 (Y): remaining 1/6, Y does 1/6, takes exactly 1 day. Finished exactly on day 5, not less than 5 days. II is incorrect.