UPSC Prelims 2023·CSAT·Quantitative Aptitude·Time and Work

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?

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Last updated 23 May 2026, 3:31 pm IST
  1. A1 onlyCorrect
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Explanation

Let total work = LCM(8, 16, 12) = 48 units. Daily output: A = 48/8 = 6, B = 48/16 = 3, C = 48/12 = 4. Per 3-day cycle (A then B then C): 6 + 3 + 4 = 13 units. After 3 full cycles (9 days), work done = 39 units; 9 units remain. The worker on each day: Day 1 Mon (A), Day 2 Tue (B), Day 3 Wed (C), Day 4 Thu (A), Day 5 Fri (B), Day 6 Sat (C), Day 7 Sun (A), Day 8 Mon (B), Day 9 Tue (C), Day 10 Wed (A), Day 11 Thu (B). Day 10 (Wed): A does 6 units → cumulative 45; 3 units remain. Day 11 (Thu): B can do up to 3 units → finishes the remaining 3 units. So the work finishes on Thursday (Statement 1 correct) and takes 11 days, not 10 (Statement 2 incorrect). Therefore, the answer is A (1 only).
Quantitative Aptitude: 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
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