The given table shows the marks obtained by 100 students out of 50 marks in Mathematics and Physics in an examination.
The given table shows the marks obtained by 100 students out of 50 marks in Mathematics and Physics in an examination.
दी गई तालिका100 छात्रों द्वारा एक परीक्षा में गणित और भौतिकी में 50 अंकों में से प्राप्त अंकों को दर्शाती हैं।

If at least 60% marks in Physics are required for pursuing higher studies in Physics, how many students will be eligible to pursue higher studies in Physics?
यदि भौतिक में उच्च शिक्षा प्राप्त करने के लिए भौतिक में कम से कम 60% अंक आवश्यक हैं, तो कितने छात्र भौतिकी में उच्च शिक्षा के लिए पात्र होंगे?
Detailed Solution & Logic
21
👉 Total marks = 50
👉 Required = 60% of 50 = $30$ marks
So, we need number of students scoring ≥ 30 marks in Physics
From the table (Physics row):
| Marks (or more) | Students |
|---|---|
| 40 या अधिक | 4 |
| 30 या अधिक | 21 |
| 20 या अधिक | 66 |
| 10 या अधिक | 81 |
| 0 या अधिक | 100 |
Important understanding:
- These are cumulative frequencies (संचयी आवृत्ति)
- “30 या अधिक” already includes students scoring 30, 40, etc.
So, students with ≥ 30 marks = 21
❗ Common mistake:
Some students subtract values (like 66 – 21), but that is used when finding range (20–30 etc.), not here.
✅ Final Answer / अंतिम उत्तर: 21
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