The following table shows the percentage (%) of colleges offering the four IT…
2022
The following table shows the percentage (%) of colleges offering the four IT courses on Python, Java, Multimedia and AI in four Indian States A-D, in a certain year. The table also presents the percentage-wise distribution of the number of Colleges in the four states. The total number of Colleges in the four states is 4000. Based on the data in the table, answer the questions 1-5.
State-wise Percentage of Colleges offering IT Courses
State | % of Colleges offering Python | % of Colleges offering Java | % of Colleges offering Multimedia | % of Colleges offering AI | % Distribution of Number of Colleges |
|---|---|---|---|---|---|
A | 86% | 74% | 59% | 56% | 35% |
B | 80% | 92% | 82% | 84% | 15% |
C | 74% | 88% | 84% | 86% | 20% |
D | 68% | 64% | 68% | 70% | 30% |
Ratio of the number of Colleges offering Multimedia in State C to that of State D is
Answer: C. 14 : 17 — ConceptTo find a subgroup count from percentage data, first multiply the total by the group's distribution percentage, then multiply that result by the…
- A.
2 : 3
- B.
1 : 13
- C.
14 : 17
- D.
13 : 16
Show answer & explanation
Correct answer: C
Concept
To find a subgroup count from percentage data, first multiply the total by the group's distribution percentage, then multiply that result by the category percentage within the group.
When two subgroup counts are compared, write them as a ratio and divide both terms by their greatest common divisor to obtain the simplest form.
Application
State C has 20% of 4000 colleges, so its total is (20/100) × 4000 = 800.
In State C, 84% of 800 colleges offer Multimedia, so the count is (84/100) × 800 = 672.
State D has 30% of 4000 colleges, so its total is (30/100) × 4000 = 1200.
In State D, 68% of 1200 colleges offer Multimedia, so the count is (68/100) × 1200 = 816.
Therefore the required ratio is 672 : 816. Dividing both terms by 48 gives 14 : 17.
Cross-check
The decimal comparison 672/816 ≈ 0.8235 agrees with 14/17 ≈ 0.8235, confirming the simplified ratio.
Result: 14 : 17.