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. Select the answer using the code given below :
- A. I only ✓
- B. II only
- C. Both I and II
- D. Neither I nor II
Correct Answer: A. I only
Explanation
Total work = LCM(4,6) = 12 units. X's rate = 3 units/day, Y's rate = 2 units/day. Starting with X: Day 1-4 complete 10 units. On the 5th day, X finishes the remaining 2 units (True). Starting with Y: Day 1-4 complete 10 units. On the 5th day, Y completes 2 units in exactly 1 full day, so it takes exactly 5 days, not less (False).
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