The answer is A.

If I select option A --> A = 24 days, B = 36 days, C = 18 days.
Work rate is: A=1/24, B=1/36, C=1/18 task/day

Now taking this statement: After A worked for 8 days, B for 12 days C takes up and finishes it alone in 6 days.

A worked for 8 days --> A finished 8/24=1/3 of the total work
B worked for 12 days --> B finished 12/36=1/3 of the total work
C worked for 6 days --> C finished 6/18=1/3 of the total work

Other options won't fit. Correct me if I am wrong.

This seems a very decent approach!

I formed the equation

72a/5 + 72b/5 = 12b + 12c = 8a + 12b + 6c

Now we have to extract 3 equations from the above and solve for 3 variables. That gets very complicated.

Set A, B, C as the rates and treat an entire piece as 1 job. Then we have the following equations:

(1) \(A + B = \frac{5}{72}\)

(2) \(B + C = \frac{1}{12}\)

(3) \(8A + 12B + 6C = 1\)

First do (3) - 8*(1) to get: \(4B + 6C = 1 - \frac{5}{9} = \frac{4}{9}\)

Subtract 4*(2) from the above to get: \(2C = \frac{4}{9} - \frac{1}{3} = \frac{1}{9}\)

Thus \(C = \frac{1}{18}\) which means C takes 18 days alone. Then we can plug this in (2) to get \(B = \frac{1}{12} - \frac{1}{18} = \frac{1}{36}\).

Now we can confirm the answer must be A.

Ans: A
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Say there are 72 units of work.

A and B together do 72/(72/5) = 5 units every day.
B and C together do 72/12 = 6 units every day.

(A worked for 8 days + B worked for 8 days) + (B worked for 4 days + C worked for 4 days) + C worked for 2 days = 72

5 * 8 + 4 * 6 + C worked for 2 days = 72

So C does 4 units of work every day. Then B does 2 units every day and A does 3 units every day.

Time taken by A = 72/3 = 24 days, by B = 72/2 = 36 days, by C = 72/4 = 18 days

Answer (A)
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