Multiple choice

A can do a certain work at twice the speed of B. Further, B can do the same work at 1.5 times the speed of C. All of them together can finish the work in 12 days. In how many days can C alone finish the work?

  1. 36 days

  2. 45 days

  3. 60 days

  4. 66 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let rate of C = c. Rate of B = 1.5c. Rate of A = 2 * (1.5c) = 3c. Combined rate = 3c + 1.5c + c = 5.5c. Work = Rate * Time = 5.5c * 12 = 66c. Time for C = Work / c = 66c / c = 66 days.

AI explanation

Let the daily work rates of A, B, and C be measured in fractions of the job. We are given that A = 2B, and B = 1.5C, which means A = 3C. Together, their combined rate is A + B + C = 3C + 1.5C + C = 5.5C. Since they finish the work in 12 days, their combined rate is 1/12 of the job per day, so 5.5C = 1/12. Solving for C's rate gives C = 1/66, meaning C alone can finish the work in 66 days.

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