A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days

B. 27 days

C. 26.67 days

D. 16 days

E. 12 days

This is my logic -

A's rate is 1/20 and B's rate is 1/30. Together they can complete the project in 12 days.

# of days the project has been completed is 'x'. Therefore, A and B work together for (x-10) days, and can complete (x-10)/12 of the project.

B alone has to complete x - (x-10)/12 of the project --> 12 x - x + 10 / 12 --> 11x + 10 / 12

So if B can complete the project in 30 days, then he can complete [(11x + 10)/12] of the project in [(11x + 10)/12]*30 days

Total time taken to complete the project would then be (x-10)/12 + (330x + 300)/12 = x

But that equation is obviously incorrect cause it gives a negative value. What have I missed?

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