The problem asks us to find the ratio between two groups of students based on their marks in Hindi and Punjabi examinations. Specifically, we need the ratio of:

• Students who scored 50 or more marks but less than 60 marks in Hindi.
• Students who scored 40 or more marks but less than 50 marks in Punjabi.

Step 1: Calculate the number of Hindi students scoring 50-59 marks

We are given the cumulative number of students who appeared in the Hindi examination scoring above certain marks.

• Cumulative number of Hindi students scoring 50 or above marks = 554.
• Cumulative number of Hindi students scoring 60 or above marks = 424.

To find the number of students who scored between 50 and 59 marks (inclusive) in Hindi, we subtract the cumulative number of students scoring 60 or above from the cumulative number of students scoring 50 or above.

Number of Hindi students (50-59 marks) = (Cumulative number scoring $\ge$ 50) - (Cumulative number scoring $\ge$ 60)

Number of Hindi students (50-59 marks) = $554 - 424 = 130$.

Step 2: Calculate the number of Punjabi students scoring 40-49 marks

First, we need to determine the total number of students (both Hindi and Punjabi combined) who scored in the specified ranges.

Total number of students who attended the exam = 1200.

From the table, the cumulative percentage of students (Hindi & Punjabi) scoring 40 or above is 100%.

Total students scoring $\ge$ 40 (Hindi or Punjabi) = $100\% \times 1200 = 1 \times 1200 = 1200$.

From the table, the cumulative percentage of students (Hindi & Punjabi) scoring 50 or above is 90%.

Total students scoring $\ge$ 50 (Hindi or Punjabi) = $90\% \times 1200 = 0.90 \times 1200 = 1080$.

Now, we find the total number of students (Hindi or Punjabi) scoring between 40 and 49 marks.

Total students (40-49 marks) = (Total students scoring $\ge$ 40) - (Total students scoring $\ge$ 50)

Total students (40-49 marks) = $1200 - 1080 = 120$.

Next, we need to find out how many of these 120 students appeared for the Punjabi exam. To do this, we first calculate the number of Hindi students who scored between 40 and 49 marks.

From the table, the cumulative number of Hindi students scoring 40 or above = 624.

From the table, the cumulative number of Hindi students scoring 50 or above = 554.

Number of Hindi students (40-49 marks) = (Cumulative Hindi students scoring $\ge$ 40) - (Cumulative Hindi students scoring $\ge$ 50)

Number of Hindi students (40-49 marks) = $624 - 554 = 70$.

Now, we can find the number of Punjabi students scoring 40-49 marks:

Number of Punjabi students (40-49 marks) = (Total students scoring 40-49) - (Hindi students scoring 40-49)

Number of Punjabi students (40-49 marks) = $120 - 70 = 50$.

Step 3: Calculate the ratio

We need the ratio of Hindi students scoring 50-59 marks to Punjabi students scoring 40-49 marks.

Ratio = (Number of Hindi students (50-59 marks)) : (Number of Punjabi students (40-49 marks))

Ratio = $130 : 50$.

To simplify the ratio, we divide both numbers by their greatest common divisor, which is 10.

Simplified Ratio = $\frac{130}{10} : \frac{50}{10} = 13 : 5$.