Multiple choice

A, B and C together can finish a piece of work in 12 days. A and C together work twice as much as B. A and B together work thrice as much as C. In what time will C finish the job alone?

  1. 36 days

  2. 48 days

  3. 28 days

  4. 32 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let rates be a, b, c. a+b+c = 1/12. a+c = 2b implies 3b = 1/12, so b = 1/36. a+b = 3c implies 4c = 1/12, so c = 1/48. C finishes in 48 days.

AI explanation

Assuming the combined daily work of A, B, and C is 1 unit, their combined rate is 1 divided by 12 per day. Since A and C together work twice as much as B, B contributes 1 unit and A plus C contribute 2 units out of the 3 units of total daily effort, meaning B's individual daily rate is 1 divided by 36. Given that A and B together work thrice as much as C, C provides 1 unit of effort while A and B provide 3 units out of 4, establishing C's daily rate as 1 divided by 48. Therefore, C alone requires 48 days to complete the job.

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