In a pie chart, the marks obtained by a student in Mathematics, Science,…
2024
In a pie chart, the marks obtained by a student in Mathematics, Science, Social Science, Hindi and English are respectively represented by sectors of central angles 90°, 80°, 65°, 75° and 50°. If the total marks obtained by the student were 540, then what is the difference of the marks obtained by him/her in Mathematics and English?
- A.
60
- B.
50
- C.
40
- D.
30
Show answer & explanation
Correct answer: A
Concept
In a pie chart, the total quantity is spread across the full circle (360°), so every degree of central angle stands for a fixed, proportional share of that total: value per degree = total quantity ÷ 360°. The quantity credited to any category equals its central angle times this per-degree rate, so the difference between two categories' quantities equals the difference of their central angles times the same rate.
Application
Confirm the sectors form a complete pie chart: 90° + 80° + 65° + 75° + 50° = 360°, so mapping 540 marks onto 360° is valid.
Find the value per degree: 540 marks ÷ 360° = 1.5 marks per degree.
Find the angle gap between the two subjects asked about: Mathematics (90°) − English (50°) = 40°.
Convert that angle gap to marks: 40° × 1.5 marks/degree = 60 marks.
Cross-check
Compute each subject's marks independently: Mathematics = 90° × 1.5 = 135 marks; English = 50° × 1.5 = 75 marks. Difference = 135 − 75 = 60 marks, confirming the shortcut above.