Understanding the Question and Data

The question asks for the ratio of the total number of male students in post-graduation courses (MSc and M.A.) to the number of male students in the PhD program. We are given a table that contains the total number of students in various courses, along with the percentage of male and female students for each course.

Analyzing the Provided Data Table

Let's look at the data provided in the table:

We need to use this table to find the required numbers of male students.

Calculating Male Students in Post-Graduation (MSc + MA)

First, we calculate the number of male students in the M.Sc. course:

• Total students in M.Sc. = 280
• Percentage of male students in M.Sc. = 75%
• Number of male students in M.Sc. = $\text{Total students} \times \frac{\text{Percentage of male students}}{100}$
• Number of male students in M.Sc. = $280 \times \frac{75}{100} = 280 \times \frac{3}{4} = 70 \times 3 = 210$

Next, we calculate the number of male students in the M.A. course:

• Total students in M.A. = 340
• Percentage of male students in M.A. = 55%
• Number of male students in M.A. = $\text{Total students} \times \frac{\text{Percentage of male students}}{100}$
• Number of male students in M.A. = $340 \times \frac{55}{100} = 340 \times \frac{11}{20} = 17 \times 11 = 187$

Now, we find the total number of male students in post-graduation (M.Sc. + M.A.):

• Total male students (M.Sc. + M.A.) = Number of male students in M.Sc. + Number of male students in M.A.
• Total male students (M.Sc. + M.A.) = $210 + 187 = 397$

Calculating Male Students in PhD Program

Now, we calculate the number of male students in the PhD program:

• Total students in PhD = 180
• Percentage of male students in PhD = 65%
• Number of male students in PhD = $\text{Total students} \times \frac{\text{Percentage of male students}}{100}$
• Number of male students in PhD = $180 \times \frac{65}{100} = 18 \times \frac{65}{10} = \frac{18 \times 65}{10} = \frac{9 \times 2 \times 13 \times 5}{2 \times 5} = 9 \times 13 = 117$

Finding the Ratio of Male Students

The question asks for the ratio of male students in post-graduation (M.Sc. + M.A.) to male students in the PhD program.

• Ratio = $\frac{\text{Total male students (M.Sc. + M.A.)}}{\text{Number of male students in PhD}}$
• Ratio = $\frac{397}{117}$

This fraction cannot be simplified further because 397 and 117 do not share common factors other than 1. (We can check for prime factors. For 117, $117 = 9 \times 13 = 3^2 \times 13$. For 397, try dividing by small primes; it's not divisible by 3, 5, 7, 11, 13, 17, 19. Checking further primes, it appears 397 is a prime number). Therefore, the ratio is $\frac{397}{117}$.

Conclusion

Based on our calculations, the ratio of male students in post-graduation (MSc + MA) and male students in the PhD program is $\frac{397}{117}$.

Revision Table - Student Data Analysis

Total male students (M.Sc. + M.A.) = $210 + 187 = 397$.

Male students (PhD) = 117.

Ratio = $\frac{397}{117}$.

Additional Information - Calculating Percentages and Ratios

Calculating a percentage of a number is a fundamental skill in data interpretation questions. The formula is:

$\text{Percentage of a number} = \text{Total} \times \frac{\text{Percentage value}}{100}$

For example, 75% of 280 is $280 \times \frac{75}{100} = 210$.

A ratio compares two quantities. If we have quantity A and quantity B, the ratio of A to B can be written as A:B or $\frac{A}{B}$. Ratios should ideally be expressed in their simplest form, although in this specific question, the options were not simplified fractions.

Data interpretation questions often require careful reading of the table and identifying exactly which numbers are needed for the calculation. Breaking down the problem into smaller steps, like calculating the number of male students for each relevant course individually, makes the process clearer and reduces the chance of errors.