Solved UPSC CDS/OTA Question
A solved UPSC CDS/OTA PYQ — decoded step-by-step.
Solve it the standard way once — then learn the shortcut.
In a class, 20% of the students were absent for an exam. 10% failed by 10 marks and 20% just passed because of grace marks of 5. Find the average score of the class if the remaining students scored an average of 50 marks and the pass marks are 30 (counting the final scores of the candidates).
Step-by-Step Solution
The complete worked solution.
Every step explained — no skipped algebra.
Let the total number of students be 100
absent students = 20% of 100 = 20
Number of students failed by 10 marks
= 10% of 100 = 10
Number of students passed by grace marks
= 20% of 100 = 20
Remaining number of students = 100 – (20 + 10 + 20) = 50
Sum of score of those students who failed by 10 marks = (30 – 10) × 10 = 200
Sum of score of those students who passed by grace marks = (30) × 20 = 600
