Understanding the Question: Ratio of Multimedia Colleges

The question asks for the ratio of the number of colleges offering the 'Multimedia' course in State C compared to State D, based on the provided table data.

The table provides two sets of information:

1. The percentage of colleges in each state offering four different IT courses (Python, Java, Multimedia, AI).
2. The percentage distribution of the total number of colleges across the four states (A, B, C, D).

The total number of colleges across all four states is given as 4000.

Analyzing the Data

First, let's understand the relevant data points from the table:

Total number of colleges = 4000

Calculating the Number of Colleges

We need to find the actual number of colleges offering Multimedia in State C and State D. This requires two steps for each state:

1. Calculate the total number of colleges in that state based on the percentage distribution of the total 4000 colleges.
2. Calculate the number of colleges offering Multimedia in that state using the percentage given for Multimedia within that state.

Step 1: Calculate Total Colleges in State C and State D

• Total Colleges in State C = Percentage distribution for State C \( \times \) Total number of colleges
• Total Colleges in State C = \( 20\% \) of \( 4000 \)
• Total Colleges in State C = \( \frac{20}{100} \times 4000 = 0.20 \times 4000 = 800 \)

• Total Colleges in State D = Percentage distribution for State D \( \times \) Total number of colleges
• Total Colleges in State D = \( 30\% \) of \( 4000 \)
• Total Colleges in State D = \( \frac{30}{100} \times 4000 = 0.30 \times 4000 = 1200 \)

Step 2: Calculate Colleges Offering Multimedia in State C and State D

• Colleges offering Multimedia in State C = Percentage of colleges offering Multimedia in State C \( \times \) Total colleges in State C
• Colleges offering Multimedia in State C = \( 84\% \) of \( 800 \)
• Colleges offering Multimedia in State C = \( \frac{84}{100} \times 800 = 0.84 \times 800 = 672 \)

• Colleges offering Multimedia in State D = Percentage of colleges offering Multimedia in State D \( \times \) Total colleges in State D
• Colleges offering Multimedia in State D = \( 68\% \) of \( 1200 \)
• Colleges offering Multimedia in State D = \( \frac{68}{100} \times 1200 = 0.68 \times 1200 = 816 \)

Finding the Ratio

Now, we need to find the ratio of the number of colleges offering Multimedia in State C to that in State D.

Ratio = (Colleges offering Multimedia in State C) : (Colleges offering Multimedia in State D)

Ratio = \( 672 : 816 \)

To simplify the ratio, we find the greatest common divisor (GCD) or divide by common factors:

• Both numbers are divisible by 8: \( 672 \div 8 = 84 \), \( 816 \div 8 = 102 \). The ratio is \( 84 : 102 \).
• Both numbers are divisible by 6: \( 84 \div 6 = 14 \), \( 102 \div 6 = 17 \). The ratio is \( 14 : 17 \).

The simplified ratio is \( 14 : 17 \).

Conclusion

The ratio of the number of colleges offering Multimedia in State C to that of State D is \( 14 : 17 \).

Revision Table: Key Calculations Summary

Ratio (State C : State D) = \( 672 : 816 = 14 : 17 \).

Additional Information: Data Interpretation and Ratios

Data interpretation questions often require extracting relevant information from tables or charts and performing calculations. This question involved percentages and ratios.

• Percentage Calculation: A percentage of a quantity is found by converting the percentage to a decimal or fraction and multiplying by the quantity. For example, P% of X is \( \frac{P}{100} \times X \).
• Ratio: A ratio compares two quantities. The ratio a:b can also be written as \( \frac{a}{b} \). Ratios should usually be simplified to their lowest terms by dividing both parts by their greatest common divisor.
• Applying Percentages Sequentially: In this problem, we first used the percentage distribution of colleges to find the base number of colleges in each state, and then applied the percentage offering a specific course (Multimedia) to that calculated base number. It's important not to directly apply the Multimedia percentage to the total 4000 colleges, as the percentages offering courses are specific to the colleges *within* each state.