While determining the classes in tally marks
Eg1: 0-10
       10-20
       20-30
Eg2: 0-10
       11-20
       21-30
Which one is correct and how to find out which one to use ?

0-10, 10-20,20-30 this type of class intervals/distribution is known as exclusive class distribution,so called because in this type of distribution we include the lower boundary point and exclude the upper boundary point(which is recorded in the consecutive next class)
The other one is known as inclusive class distribution since you include all the values along with the lower and upper boundary points. 

NOTE;THE CHOICE DEPENDS UPON THE QUESTION. IN MOST OF THE CASES, THE TYPE OF DISTRIBUTION TO BE USED IS CLEARLY SPECIFIED IN THE QUESTION ITSELF.