In a class, 20% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed.Find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40.45493640

To solve this problem, we need to break it down into several steps:

1. First, let's identify the different groups of students:

   • 20% were absent.
   • 30% failed by 20 marks.
   • 10% just passed.
   • The remaining students (which is 100% - 20% - 30% - 10% = 40%) scored an average of 65 marks.

2. Next, let's find out the scores for the students who failed and those who just passed:

   • The students who failed scored 20 marks less than the cut off, which is 40.45493640 - 20 = 20.45493640 marks.
   • The students who just passed scored exactly at the cut off, which is 40.45493640 marks.

3. Now, we can calculate the average score of the class. The average score is the total score divided by the number of students. Since we don't know the exact number of students, we can assume there are 100 students for simplicity (this won't affect the average). So the total score is:

   • 20 students were absent, so they contribute 0 to the total score.
   • 30 students failed, so they contribute 30 * 20.45493640 = 613.648092 marks.
   • 10 students just passed, so they contribute 10 * 40.45493640 = 404.549364 marks.
   • 40 students scored an average of 65 marks, so they contribute 40 * 65 = 2600 marks.

4. Adding these up, the total score is 0 + 613.648092 + 404.549364 + 2600 = 3618.197456 marks.

5. Finally, the average score of the class is the total score divided by the number of students, which is 3618.197456 / 100 = 36.18197456 marks.