Let's solve this problem step by step.

1. Given Information:

   • The average marks of 19 students = 76
   • After adding one more student, the average decreases by 2, so the new average = 74

2. Calculations:

   • Step 1: Total marks of 19 students: $\text{Total marks of 19 students} = 76 \times 19 = 1444$

   • Step 2: Total marks of 20 students (after including the new student): $\text{Total marks of 20 students} = 74 \times 20 = 1480$

   • Step 3: Marks of the new student: $\text{Marks of the new student} = \text{Total marks of 20 students} - \text{Total marks of 19 students}$ $\text{Marks of the new student} = 1480 - 1444 = 36$

So, the marks of the new student are 36.

Would you like further details or have any questions?

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Here are some related questions to further explore the topic:

1. How would the result change if the average increased by 2 instead of decreased?
2. What if the number of initial students was 25 instead of 19?
3. How can we find the new average if the new student scored the same as the previous average?
4. What happens to the total marks if two more students are added with different marks?
5. How can you express the solution as an algebraic equation?
6. If the average was calculated incorrectly, how would you approach correcting it?
7. What is the impact of the new student's marks being below the average on the group's performance?
8. How can this problem be generalized to include any number of students and changes in average?

Tip: Always check your steps by back-substituting the final answer into the original problem to ensure accuracy.