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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 ?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
To solve the problem, let's calculate how much work is done each day:
- A's rate of working: 1/8 of the work per day.
- B's rate of working: 1/16 of the work per day.
- C's rate of working: 1/12 of the work per day.
The pattern repeats every three days, so let's calculate the work done in the first three days:
- Monday (A): 1/8
- Tuesday (B): 1/16
- Wednesday (C): 1/12
Total work done in 3 days:
18+116+112=648+348+448=1348
Now, let's find out how many such 3-day cycles are needed to complete the work:
- Work done in 6 days (first two cycles):
2×1348=2648
- Seventh day (A): 1/8
Work done by A on Thursday: 18=648
Adding this on the seventh day:
2648+648=3248
- Eighth day (B): 1/16
Work done by B on Friday: 348
Adding this on the eighth day:
3248+348=3548
- Ninth day (C): 1/12
Work done by C on Saturday: 448
Adding this on the ninth day:
3548+448=3948
Finally, on the tenth day (A), he completes:
648
Total work by tenth day:
3948+648=1
- The work is finished on the tenth day.
Review of Statements
- Statement 1: The work will be finished on Thursday. (Incorrect, it finishes on the following Monday)
- Statement 2: The work will be finished in 10 days. (Correct)
Conclusion:
- The correct option is: 2, 2 only.
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