Multiple choice

At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

  1. 24 days

  2. 18 days

  3. 12 days

  4. 36 days

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A's 1 day work = 1/a, B's 1 day work = 1/b. Normal: 1/a + 1/b = 1/12. Modified: 1/(2a) + 3/b = 1/9. Multiply first eq by 18: 18/a + 18/b = 3. Multiply second eq by 36a: 18 + 108a/b = 4a. Substituting and solving gives a = 18, so A alone takes 18 days.

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