Marks-wise distribution of studentsMarks (Out of 100) Cumulative precentage of the total number of students who appeared in Hindi and Punjabi Cumulative number of students who appeared in Hindi 80 and above 15% 108 70 and above 35% 264 60 and above 65% 424 50 and above 90% 554 40 and above 100% 624
Note:
(1) Total number of students who attended the exam is 1200.
(2) No student failed in the examination.
(3) Each student appeared in only one exam, that is, either in Hindi or in Punjabi exam.
Exam Data Overview
This problem requires us to analyze the provided table which shows the cumulative percentage of students appearing in Hindi and Punjabi examinations, along with the cumulative number of students appearing in the Hindi examination across different mark categories. We are given that the total number of students is 1200, no student failed, and each student took either the Hindi or the Punjabi exam.
Data Table
| Marks (Out of 100) | Cumulative percentage of the total number of students who appeared in Hindi and Punjabi | Cumulative number of students who appeared in Hindi |
|---|---|---|
| 80 and above | 15% | 108 |
| 70 and above | 35% | 264 |
| 60 and above | 65% | 424 |
| 50 and above | 90% | 554 |
| 40 and above | 100% | 624 |
Solution Steps for Hindi Punjabi Exam
Hindi Students Scoring 80+
The question asks for the number of students who scored 80 and above marks in Hindi. Looking at the table, the row for "80 and above" shows the "Cumulative number of students who appeared in Hindi" as 108. This value directly represents the number of students who achieved 80 marks or more in the Hindi examination.
Number of Hindi students (80 and above) = 108.
Punjabi Students 60-69 Marks
To find the number of students who scored 60 or more than 60 marks but less than 70 marks in Punjabi, we need to perform a few calculations:
- First, calculate the total number of students (Hindi + Punjabi) who scored 60 and above.
- Then, subtract the number of Hindi students who scored 60 and above from this total to get the number of Punjabi students who scored 60 and above.
- Next, calculate the total number of students (Hindi + Punjabi) who scored 70 and above.
- Then, subtract the number of Hindi students who scored 70 and above from this total to get the number of Punjabi students who scored 70 and above.
- Finally, subtract the number of Punjabi students scoring 70 and above from the number of Punjabi students scoring 60 and above to find those in the 60-69 range.
Punjabi Students $\ge 60$ Calculation
From the table:
- Cumulative percentage of students (Hindi + Punjabi) scoring 60 and above = 65%.
- Total number of students = 1200.
- Total number of students (Hindi + Punjabi) scoring 60 and above = $0.65 \times 1200 = 780$.
- Cumulative number of Hindi students scoring 60 and above = 424.
- Therefore, the number of Punjabi students scoring 60 and above = Total (Hindi + Punjabi) $\ge 60$ - Number (Hindi) $\ge 60$.
- Number of Punjabi students (60 and above) = $780 - 424 = 356$.
Punjabi Students $\ge 70$ Calculation
From the table:
- Cumulative percentage of students (Hindi + Punjabi) scoring 70 and above = 35%.
- Total number of students = 1200.
- Total number of students (Hindi + Punjabi) scoring 70 and above = $0.35 \times 1200 = 420$.
- Cumulative number of Hindi students scoring 70 and above = 264.
- Therefore, the number of Punjabi students scoring 70 and above = Total (Hindi + Punjabi) $\ge 70$ - Number (Hindi) $\ge 70$.
- Number of Punjabi students (70 and above) = $420 - 264 = 156$.
Punjabi Students 60-69 Calculation
The number of students scoring 60 or more than 60 marks but less than 70 marks in Punjabi is calculated by subtracting the number of Punjabi students scoring 70 and above from the number of Punjabi students scoring 60 and above.
Number of Punjabi students (60 to 69 marks) = Number of Punjabi students (60 and above) - Number of Punjabi students (70 and above)
Number of Punjabi students (60 to 69 marks) = $356 - 156 = 200$.
Percentage Difference Calculation
We need to find how much percentage less the number of Hindi students (80 and above) is compared to the number of Punjabi students (60 to 69 marks).
Difference in number = Number of Punjabi students (60-69) - Number of Hindi students (80+)
Difference = $200 - 108 = 92$.
Percentage less = $\frac{\text{Difference}}{\text{Number of Punjabi students (60-69)}} \times 100$
Percentage less = $\frac{92}{200} \times 100$
Percentage less = $0.46 \times 100 = 46\%$.
Final Answer Hindi Punjabi
The number of students who scored 80 and above marks in Hindi is 46% less than the number of students who scored 60 or more than 60 marks but less than 70 marks in Punjabi.
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