A clock is set right at 8 am. The clock gains 8 minutes in a day. What will be the true time when the watch indicates 11 am the next day?

It is given clock is set right at 8 am . 
Clock gains 8 mins a day . 

       $$\rightarrow$$ Addition of 8 mins a day is equivalent to adding 1 min per 3 hours . (as in a day there are total 24 hrs). 

Now we are supposed to find the true time when clock shows 11 am on the next day : 
In a span of 24 hours , the clock gains 8 mins.. So, after 24 hrs i.e next day the time on clock would be 8:08 am ..

After this particular time of 8:08 am , lets say after exactly "t" hours the clock shows 11 am .. But we already know that every hour there is $$\ \dfrac{\ 1}{3}$$min increment which is nothing but $$\dfrac{\ 1}{180}\ hr\ $$ per every hour. Hence : 

                                    8:08 am + t + $$\ \dfrac{\ t}{180}$$ = 11:00 am 

                                             t(1+ 0.00555) = 2 hrs 52 mins = 2.866 hrs. 

                                             Therefore, $$t=\dfrac{\ 2.866}{1.0055}=2.850$$ hours. 

Therefore, the original time will be = 8:00 am + 2.850 hrs = 10 : 51 am .