Multiple choice

A is 40% less efficient than B who can do the same work in 20% less time than C. If A and B together can complete 80% work in 12 days, then in how many days 60% work can be completed by B and C together?

  1. 2 days

  2. 4 days

  3. 8 days

  4. 16 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Efficiency A = 0.6 * Efficiency B. Time B = 0.8 * Time C, so Efficiency B = 1/0.8 * Efficiency C = 1.25 * Efficiency C. A+B complete 80% in 12 days, so 100% in 15 days. (Eff A + Eff B) = 1/15. 0.6B + B = 1/15 -> 1.6B = 1/15 -> B = 1/24. C = B/1.25 = 1/30. B+C efficiency = 1/24 + 1/30 = (5+4)/120 = 9/120 = 3/40. Time for 60% work = 0.6 / (3/40) = 0.6 * 40 / 3 = 8 days.

AI explanation

Because A is 40% less efficient than B, A's efficiency is 0.6 times B's efficiency. Let the work done by A and B in one day be 0.6x and x respectively. Since A and B together complete 80% of the work in 12 days, their combined daily work is 0.8 / 12 = 1 / 15 of the total work. Therefore, 0.6x + x = 1.6x = 1 / 15, which means x = 1 / 24 and B alone takes 24 days. B takes 20% less time than C, meaning B's time is 0.8 times C's time, so C takes 24 / 0.8 = 30 days. The combined daily work of B and C is (1 / 24) + (1 / 30) = 3 / 40 of the total task. To complete 60% of the work, they require (3 / 5) / (3 / 40) = 8 days.

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