Multiple choice

A can do a piece of work in 10 days and B can do the same work in 15 days. A and B start a work together. A works at 1/3rd of his usual efficiency and B works at half of his usual efficiency. How many days will they take to complete a piece of work which is twice as large as the original work?

  1. 15

  2. 30

  3. 12

  4. 10

  5. 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's usual rate = 1/10, B's = 1/15. New rates: A = 1/30, B = 1/30. Combined rate = 2/30 = 1/15. To do twice the work (2 units), time = 2 / (1/15) = 30 days.

AI explanation

A's original 1 day work is 1/10, and B's is 1/15; working at 1/3rd and half their respective efficiencies, their new 1 day works become 1/30 and 1/30. Adding these efficiencies, their combined 1 day work is 1/15 of the original job. Since the new piece of work is twice as large, dividing this doubled work (2 units) by their daily work rate (1/15 unit per day) results in 30 days.

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