Multiple choice

A is twice as efficient as B and B is twice as efficient as C. Time taken by C and D together to complete a piece of work is 4 days. If D takes 6 days to complete the same work alone, then how much time will A alone take to complete the same work?

  1. 3 days

  2. 2 days

  3. 4 days

  4. 5 days

  5. 1 day
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Efficiency: A = 2B, B = 2C, so A = 4C. Let C's rate be c. A=4c, B=2c, C=c. C+D take 4 days, so c + d = 1/4. D takes 6 days, so d = 1/6. c = 1/4 - 1/6 = 3/12 - 2/12 = 1/12. A's rate = 4c = 4/12 = 1/3. A takes 3 days.

AI explanation

Let the work done by C, B, and A in one day be x, 2x, and 4x respectively. Using the combined work formula, C and D together complete the work in 4 days, meaning their one day work is 1/4. Since D alone takes 6 days, D's one day work is 1/6, which makes C's one day work (1/4 - 1/6) equal to 1/12. Since C takes 12 days alone and A is four times as efficient as C, A alone takes 12 divided by 4 days. The result is 3 days.

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