Theory:

Case I: If the given times are in \(24\)-hour format, you can directly subtract those times and find the duration.
 
Case II: If the given times are in \(12\)-hour format, first convert them into \(24\)-hour format, and then subtract those times and find the duration.
Example:
1. Calculate the duration between \(10\!:\!40\) hours to \(16\!:\!15\) hours.
 
Solution:
 
Starting time \(=\) \(10\!:\!40\) hours
 
Ending time \(=\) \(16\!:\!15\) hours
 
Duration \(=\) Ending time \(-\) Starting time
 
\(=\) \(16\!:\!15\) \(-\) \(10\!:\!40\)
 
16:1510:40¯
 
Here, \(40\) minutes cannot be subtracted from \(15\) minutes.
 
So, borrow \(1\) hour from \(16\) hours, add this to \(15\) minutes.
 
\(1\) hour \(+\) \(15\) minutes:
 
\(=\) \(60\) minutes \(+\) \(15\) minutes
 
\(=\) \(75\) minutes
 
Now, subtract \(15\!:\!75\) hours from \(10\!:\!40\) hours.
 
157516:1510:405:35¯¯
 
Therefore, duration between \(10\!:\!40\) hours to \(16\!:\!15\) hours is \(5\) hours \(35\) minutes.
 
 
2. Find the duration between \(11\!:\!20\) a.m. to \(5\!:\!30\) p.m.
 
Solution:
 
Let us first convert the given times to \(24\)-hour format.
 
Starting time \(=\) \(11\!:\!20\) a.m. \(=\) \(11\!:\!20\) hours
 
Ending time \(=\) \(5\!:\!30\) p.m. \(=\) \(5\!:\!30\) \(+\) \(12\!:\!00\) \(=\) \(17\!:\!30\) hours
 
Duration \(=\) Ending time \(-\) Starting time
 
\(=\) \(17\!:\!30\) hours \(-\) \(11\!:\!20\) hours
 
17:3011:206:10¯¯
 
Therefore, the duration between \(11\!:\!20\) a.m. to \(5\!:\!30\) p.m. is \(6\) hours \(10\) minutes.