In a city there are few under - graduate , graduate and post - graduate…
2024
In a city there are few under - graduate , graduate and post - graduate candidates . Sum of four times the undergraduate , three times the graduate and five times the post graduates is 3650 . Also three times post - graduates is equal to two times graduates . Also Three times post graduates is equal to two times graduates . Three times the under graduates is equal to two times the post graduates . Total how many post graduates are there in a city ?
- A.
300
- B.
250
- C.
550
- D.
450
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Correct answer: A
Answer: 300
Let the number of undergraduates = u, graduates = g, and postgraduates = p.
Given: 4u + 3g + 5p = 3650.
From the relations: 3p = 2g ⇒ g = 3p/2, and 3u = 2p ⇒ u = 2p/3.
Substitute u and g in terms of p into the sum: 4*(2p/3) + 3*(3p/2) + 5p = 3650.
Simplify: (8p/3) + (9p/2) + 5p = (16p + 27p + 30p)/6 = (73/6)p = 3650.
Solve for p: p = 3650 * 6 / 73 = 21900 / 73 = 300. Therefore there are 300 postgraduates.