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A group of 120 students, 90 take mathematics and 72 take economics. If 10 students take neither of the two, how many students take both:
- a)20
- b)62
- c)32
- d)30
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A group of 120 students, 90 take mathematics and 72 take economics. If...
Total number of students :120
Mathematics :90
Economics :72
Neither mathematics nor economics:10
Students who took both subject =90+72-120-10 = 32
Most Upvoted Answer
A group of 120 students, 90 take mathematics and 72 take economics. If...
Understanding the Problem
We have a total of 120 students. Out of these:
- 90 students take Mathematics.
- 72 students take Economics.
- 10 students take neither subject.
Calculating Students Taking at Least One Subject
First, we need to find out how many students take at least one subject:
- Total students = 120
- Students taking neither = 10
Using this, we can calculate:
- Students taking at least one subject = Total students - Students taking neither
= 120 - 10 = 110
Using the Principle of Inclusion-Exclusion
Let:
- n(M) = Number of students taking Mathematics = 90
- n(E) = Number of students taking Economics = 72
- n(M ∪ E) = Number of students taking at least one subject = 110
- n(M ∩ E) = Number of students taking both subjects
Using the formula for the union of two sets:
n(M ∪ E) = n(M) + n(E) - n(M ∩ E)
Substituting the known values:
110 = 90 + 72 - n(M ∩ E)
Now, simplifying:
110 = 162 - n(M ∩ E)
This leads us to:
n(M ∩ E) = 162 - 110 = 52
Conclusion
Thus, the number of students taking both Mathematics and Economics is:
52 students
Therefore, the correct answer is option 'C'.
We have a total of 120 students. Out of these:
- 90 students take Mathematics.
- 72 students take Economics.
- 10 students take neither subject.
Calculating Students Taking at Least One Subject
First, we need to find out how many students take at least one subject:
- Total students = 120
- Students taking neither = 10
Using this, we can calculate:
- Students taking at least one subject = Total students - Students taking neither
= 120 - 10 = 110
Using the Principle of Inclusion-Exclusion
Let:
- n(M) = Number of students taking Mathematics = 90
- n(E) = Number of students taking Economics = 72
- n(M ∪ E) = Number of students taking at least one subject = 110
- n(M ∩ E) = Number of students taking both subjects
Using the formula for the union of two sets:
n(M ∪ E) = n(M) + n(E) - n(M ∩ E)
Substituting the known values:
110 = 90 + 72 - n(M ∩ E)
Now, simplifying:
110 = 162 - n(M ∩ E)
This leads us to:
n(M ∩ E) = 162 - 110 = 52
Conclusion
Thus, the number of students taking both Mathematics and Economics is:
52 students
Therefore, the correct answer is option 'C'.
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A group of 120 students, 90 take mathematics and 72 take economics. If 10 students take neither of the two, how many students take both:a)20b)62c)32d)30Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A group of 120 students, 90 take mathematics and 72 take economics. If 10 students take neither of the two, how many students take both:a)20b)62c)32d)30Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A group of 120 students, 90 take mathematics and 72 take economics. If 10 students take neither of the two, how many students take both:a)20b)62c)32d)30Correct answer is option 'C'. Can you explain this answer?.
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