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% |
If M and N represent the total number of Colleges offering Python and Java, respectively, in all the four states, then M-N=
Answer: D. 32 — ConceptWhen a total is divided among groups, the number in a group equals the total multiplied by that group’s distribution percentage. A second percentage…
- A.
64
- B.
96
- C.
48
- D.
32
Show answer & explanation
Correct answer: D
Concept
When a total is divided among groups, the number in a group equals the total multiplied by that group’s distribution percentage. A second percentage within that group is then applied to obtain the required subgroup count.
For a state with share s% and course-offering rate r%, the required count is Total × s/100 × r/100. Compute each state separately and then add the results.
Application
The numbers of colleges in States A, B, C and D are 4000 × 35% = 1400, 4000 × 15% = 600, 4000 × 20% = 800 and 4000 × 30% = 1200, respectively.
Python total: M = 1400 × 86% + 600 × 80% + 800 × 74% + 1200 × 68% = 1204 + 480 + 592 + 816 = 3092.
Java total: N = 1400 × 74% + 600 × 92% + 800 × 88% + 1200 × 64% = 1036 + 552 + 704 + 768 = 3060.
Therefore, M − N = 3092 − 3060 = 32 colleges.
Cross-check
Compute the difference directly by state: 1400 × 12% + 600 × (−12%) + 800 × (−14%) + 1200 × 4% = 168 − 72 − 112 + 48 = 32. This agrees with the difference of the two totals.