$12$ men can finish a job in $16$ days. $5$ men work at the start; and after 8 days, 3 men were added. How many days needed to finish the whole job? 
Twelve men can finish a job in 16 days. 5 men were working at the start and after 8 days, 3 men were added. How many days will it take to finish the whole job?

Solution:
So, the job will take $12 \times 16 = 192$ man days to finish.
In the first $8$ days we have done $8 \times 5 = 40$ man days.
Now we are doing $8 \times 8 = 64$ man days per day and need to do the remaining $192 - 40 = 152 $man days.


*

*Day $1 = 152 - 64 = 88$ man days left

*Day $2 = 88 - 64 = 24$
So, we’ll finish on day $3$ after the extra $3$ men are added.
So based on my solution, I came up with $11$ days but I feel like it's wrong. Can someone point out my mistakes if any? 

In steps:
$1$ man can finish the job in $12×16$ days.
$1$ man works  $1$ day to finish $1/(12×16)$ of the job.
$5$ man work $8$ days to finish $(5×8)/(12×16)=5/24$ of the job.
$19/24$ of the job left to complete by $8$ people.
Let $X$ be the number of days.
$(8/(12×16))×X=19/24$;
$X= 19$;
Altogether:
$8+19=27$ days.
