Multiple choice

C completes work in 15 days. How many days A, B, C together? I: A & B together 5.625 days. II: B & C together 9 days.

  1. I alone sufficient

  2. II alone sufficient

  3. Either I or II sufficient

  4. Both not sufficient

  5. Both necessary
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A Correct answer
Explanation

We know C's rate is 1/15. Statement I gives A+B's rate as 1/5.625 = 16/90 = 8/45. Together A+B+C = 8/45 + 3/45 = 11/45. This is sufficient. Statement II gives B+C's rate as 1/9. We don't know A's rate. Thus, I alone is sufficient.

AI explanation

From the question, C's 1 day work is 1/15, and the target is to find the combined rate of A, B, and C. Statement I provides the combined rate of A and B as 1/5.625, which allows us to calculate the combined rate of all three by adding C's rate to A and B's rate. Statement II only gives the rate of B and C, which is insufficient to find the rate of A. Therefore, Statement I alone is sufficient to find the answer.

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