Interpreting Exam Data: Hindi and Punjabi Students

This problem requires us to calculate the average number of students who scored between 50 and 59 marks in both the Hindi and Punjabi examinations. We need to use the provided data, which includes the cumulative percentage of students for Hindi and Punjabi combined, and the cumulative number of students specifically for the Hindi examination.

Calculating Hindi Students (50-59 Marks)

First, let's find the number of students who scored 50 or more marks in the Hindi exam and the number of students who scored 60 or more marks in the Hindi exam. Then, we can find the difference to get the count for the 50-59 marks range.

• From the table, the cumulative number of students scoring 50 and above in Hindi is 554.
• The cumulative number of students scoring 60 and above in Hindi is 424.
• The number of students scoring 50 or more but less than 60 marks in Hindi is the difference between these two values.

Calculation for Hindi Students (50-59 marks):

Number of Hindi students (Marks $\ge 50$) = 554

Number of Hindi students (Marks $\ge 60$) = 424

Number of Hindi students ($50 \le \text{Marks} < 60$) = Number of Hindi students (Marks $\ge 50$) - Number of Hindi students (Marks $\ge 60$)

Number of Hindi students ($50 \le \text{Marks} < 60$) = $554 - 424 = 130$ students.

Calculating Punjabi Students (50-59 Marks)

Next, we need to find the number of students who scored 50-59 marks in the Punjabi exam. To do this, we first find the total number of students (Hindi + Punjabi) who scored in this range using the cumulative percentages, and then subtract the number of Hindi students we just calculated.

Total students who appeared for the exam = 1200.

• The cumulative percentage of students scoring 50 and above (Hindi & Punjabi) is 90%.
• The cumulative percentage of students scoring 60 and above (Hindi & Punjabi) is 65%.

Calculate the total number of students scoring 50 or more:

Total students (Marks $\ge 50$) = $90\%$ of 1200

Total students (Marks $\ge 50$) = $\frac{90}{100} \times 1200 = 1080$ students.

Calculate the total number of students scoring 60 or more:

Total students (Marks $\ge 60$) = $65\%$ of 1200

Total students (Marks $\ge 60$) = $\frac{65}{100} \times 1200 = 780$ students.

Now, find the total number of students scoring 50-59 marks (Hindi & Punjabi combined):

Total students ($50 \le \text{Marks} < 60$) = Total students (Marks $\ge 50$) - Total students (Marks $\ge 60$)

Total students ($50 \le \text{Marks} < 60$) = $1080 - 780 = 300$ students.

Since each student appeared in only one exam (Hindi or Punjabi), the number of Punjabi students scoring 50-59 marks can be found by subtracting the Hindi students in this range from the combined total:

Number of Punjabi students ($50 \le \text{Marks} < 60$) = Total students ($50 \le \text{Marks} < 60$) - Number of Hindi students ($50 \le \text{Marks} < 60$)

Number of Punjabi students ($50 \le \text{Marks} < 60$) = $300 - 130 = 170$ students.

Calculating the Average

Finally, we need to find the average of the number of students who scored 50-59 marks in Punjabi and the number of students who scored 50-59 marks in Hindi.

• Number of Punjabi students (50-59 marks) = 170
• Number of Hindi students (50-59 marks) = 130

Average = $\frac{\text{Number of Punjabi students (50-59)} + \text{Number of Hindi students (50-59)}}{2}$

Average = $\frac{170 + 130}{2}$

Average = $\frac{300}{2}$

Average = 150 students.

Summary of Key Data

Based on the calculations, the average number of students scoring 50-59 marks in Punjabi and Hindi is 150.