Multiple choice

A and B work together for 8 days to complete a piece of work and B and C work together for 12 days to complete the same work. C alone can complete the work in 24 days and A is twice as efficient as B. How much time does it take to complete the work if all the three work together?

  1. 8 days

  2. 6 days

  3. 15 days

  4. 16 days

  5. 20 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A+B = 1/8, B+C = 1/12, C = 1/24. B = 1/12 - 1/24 = 1/24. A = 2 * B = 2/24 = 1/12. A+B+C = 1/12 + 1/24 + 1/24 = 2/24 + 1/24 + 1/24 = 4/24 = 1/6. Time = 6 days.

AI explanation

Let the work be 1 unit. Using the given efficiencies, if B's rate is r, A's rate is 2r and C's rate is (1/24). From the first condition, 8(2r + r) = 1, giving r = 1/24, so A's rate is 1/12. From the second condition, 12(r + 1/24) = 1, which gives r = 1/24. Since all conditions match perfectly, their combined rate is (1/12 + 1/24 + 1/24) = 1/6 of the work per day. Therefore, they complete the work together in 6 days.

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