A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements:
- 1.The work will be finished on Thursday.
- 2.The work will be finished in 10 days.
Which of the above statements is/are correct?
Answer & explanation
Answer: (a) 1 only
Take the work as 48 units: A does 6, B 3 and C 4 units a day, so each 3-day round finishes 13 units. After 9 days 39 units are done; A adds 6 on day 10 and B completes the last 3 on day 11. Counting from Monday, day 11 is a Thursday.
- Total work = LCM(8, 16, 12) = 48 units. A does 6, B does 3 and C does 4 units a day.
- One round (A, B, C) = 6 + 3 + 4 = 13 units in 3 days. After 3 rounds (9 days): 39 units, so 9 units remain.
- Day 10 (A): 39 + 6 = 45 units. Day 11 (B): 45 + 3 = 48 units — the work is complete.
- Day 1 is Monday, so day 8 is Monday again and day 11 is Thursday.
- Statement 1 is correct; statement 2 is not, because the work takes 11 days.
- ✓ 1. The work ends on day 11, and day 11 counted from a Monday is a Thursday.
- ✗ 2. After 10 days only 45 of the 48 units are done; B needs day 11 to finish.
Remember · Take the LCM of days as total work, add round by round, then day by day; convert day numbers to weekdays using remainders by 7.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·