In an engineering college of 10,000 students, 1,500 like neither their core…
2024
In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500. The number of students who like their core branches is
- A.
1,800
- B.
3,500
- C.
1,600
- D.
1,500
Attempted by 37 students.
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Correct answer: A
Solution:
Total students = 10,000. Students who like neither = 1,500, so students who like at least one branch = 10,000 - 1,500 = 8,500.
Let C = number who like core branches, O = number who like other branches. Given C = (1/4)O and the number who like both = 500.
Use the union formula: C + O - (both) = students who like at least one. So C + O - 500 = 8,500, hence C + O = 9,000.
Substitute C = O/4: (O/4) + O = 9,000 ⇒ (5O/4) = 9,000 ⇒ O = 9,000 × 4 / 5 = 7,200.
Therefore C = O/4 = 7,200 / 4 = 1,800.
Answer: 1,800.
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