Question: > 
> It takes 36 days for Mr. A to complete a certain task, and 18 days for
>  Mr. B to complete the same task. When Mr. A performs the task together
>  with Mr. B, approximately how many days does it take to complete the
>  task? Here, the task can be divided and performed in parallel, and
>  both Mr. A and Mr. B can achieve an average working efficiency of 90 %
>  every day during the cooperative task
> 
> 
> 

Mr A finishes the task in 36 days, so every day he completes 1/36 the works of the task 

Mr B finishes the task in 18 days, so every day he completes 1/18 the works of the task 

When the 2 of them working together on a task : 1/36 + 1/18 = 1, which gives me the result of 10.8 days for them to finish the task. 

But the right answer is 14 days. Can you point out what am I missing here? Thanks!

Answer: 
If the number of days is $n$ then $\frac{9}{10}n(\frac{1}{18} + \frac{1}{36}) = 1$ by your reasoning. The extra $\frac{9}{10}$ is for their efficiency.

Isolating $n$ then gives $n = \frac{40}{3} = 13.33$ days. So they finish during the 14th day.
If two guys at 100% efficiency would take 12 days to finish the task, as you calculated, then if they work at only 90% efficiency it will take them *longer* than 12 days to finish. But your answer of 10.8 days says that they can finish the task *faster* by working together.