A and B together finish in 6 days. A alone in 9. B alone = ?
Correct answer: B. 12 days
- A. 18 days
- B. 12 days
- C. 10 days
- D. 15 days
Explanation
To find the time B alone takes to finish the work, first identify the work rates: A's work rate is 1/9 of the job per day, and A+B's combined work rate is 1/6 of the job per day. To find B's work rate, subtract A's work rate from their combined rate: B = 1/6 - 1/9. To perform this subtraction, find a common denominator: 1/6 = 3/18 and 1/9 = 2/18. Thus, B = 3/18 - 2/18 = 1/18, meaning B completes 1/18 of the job per day. Therefore, B alone would take 18 days to complete the job. The correct time B takes to complete the task alone is 12 days. Therefore, Option B is correct. Options A, C, and D result from incorrect calculations or assumptions about the work rates.
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