The following table gives the percentage of marks obtained by seven students…
2023
The following table gives the percentage of marks obtained by seven students in six different subjects in an examination.The Numbers in the Brackets give the Maximum Marks in Each Subject.
What is the overall percentage of Tarun?
- A.
52.5%
- B.
55%
- C.
60%
- D.
63%
Show answer & explanation
Correct answer: C
Concept: When a data-interpretation table lists the PERCENTAGE of marks obtained in each subject, with each subject's own maximum marks given in brackets, a student's overall percentage is NOT the plain average of the six percentages. Each percentage must first be converted into actual marks obtained (percentage times maximum divided by 100), because the subjects carry different maximum marks. The overall percentage is then (total marks obtained across all subjects divided by total maximum marks across all subjects) times 100.
Application — Tarun's aggregate:
Maths: 65% of 150 = 97.5
Chemistry: 35% of 130 = 45.5
Physics: 50% of 120 = 60
Geography: 77% of 100 = 77
History: 80% of 60 = 48
Computer Science: 80% of 40 = 32
Total marks obtained = 97.5 + 45.5 + 60 + 77 + 48 + 32 = 360
Total maximum marks = 150 + 130 + 120 + 100 + 60 + 40 = 600
Overall percentage = (360 / 600) x 100 = 60%
Cross-check: 360/600 simplifies to 3/5, and 3/5 of 100 is exactly 60, confirming the figure. Also note that the plain (unweighted) average of Tarun's six percentages — (65 + 35 + 50 + 77 + 80 + 80) / 6 = 64.5% — is different from the correct 60%, which confirms why weighting by each subject's maximum marks (not a simple average) is required whenever subjects carry different maximum marks.