Multiple choice

A is thrice as efficient as B. Working together, they complete the work in 3 days. If working alone, B takes 8 days more than A to finish the whole work. What is the number of days taken by A to finish the whole work alone?

  1. 6

  2. 4

  3. 8

  4. 12

  5. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A take x days, then B takes 3x days. Together: 1/x + 1/3x = 1/3, so 4/3x = 1/3, x = 4. B takes 12 days, which is 8 days more than A (4 days).

AI explanation

Using the standard work equation where A's rate is 1/x and B's rate is 1/(x+8), their combined rate is 1/3. Substituting A being thrice as efficient as B means 1/x = 3/(x+8), which simplifies to x+8 = 3x, making x = 4. We can verify this because if A takes 4 days (rate 1/4) and B takes 12 days (rate 1/12), their combined rate is 1/4 + 1/12 = 4/12, which perfectly equals 1/3. Therefore, A takes 4 days alone.

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