Alternating time and work schedule (A, B, C)
Question
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:
Which of the above statements is/are correct?
Options
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Explanation
Determine total work by finding the LCM of individual timelines: LCM(8, 16, 12) = 48 units . Compute individual daily output rates: A = 48 / 8 = 6 units/day B = 48 / 16 = 3 units/day C = 48 / 12 = 4 units/day
They work in a strict rotational cycle: Day 1 (A), Day 2 (B), Day 3 (C). Output per 3-day cycle = 6 + 3 + 4 = 13 units.
Track progress cycle by cycle:
Now map out the 4th cycle starting on Day 10:
The work finishes exactly at the end of Day 11. Let's check the week-day map starting on Monday: Day 10 is Wednesday, and Day 11 is Thursday. Thus, Statement 1 is Correct. Total days required is 11, making Statement 2 Incorrect.
Self-Correction Check on Option mapping: Statement 1 says "finished on Thursday", which matches our day-of-week calculation. Statement 2 says "finished in 10 days", which is false. Thus, only Statement 1 is correct.
Answer: (a).
Question details
Year
2023
Paper
CSAT
Question
Q20
Section
Numerical Ability
Sub-topic
Time & Work
Type
Arithmetic word problem
Difficulty
Medium
Source hint
Time-work application
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