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In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?
- a)5%
- b)15%
- c)0%
- d)25%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a class 40% of the students enrolled for Math and 70% enrolled for ...
We know that (A ∪ B) = A + B - (A ∩ B), where (A ∪ B) represents the set of people who have enrolled for at least one of the two subjects Math or Economics and (A ∩ B) represents the set of people who have enrolled for both the subjects Math and Economics.
(A ∪ B) = A + B - (A ∩ B)
⇒ (A ∪ B) = 40% + 70% - 15% = 95%
That is 95% of the students have enrolled for at least one of the two subjects Math or Economics.
Therefore, the balance (100 - 95) % = 5% of the students have not enrolled for either of the two subjects.
(A ∪ B) = A + B - (A ∩ B)
⇒ (A ∪ B) = 40% + 70% - 15% = 95%
That is 95% of the students have enrolled for at least one of the two subjects Math or Economics.
Therefore, the balance (100 - 95) % = 5% of the students have not enrolled for either of the two subjects.
Most Upvoted Answer
In a class 40% of the students enrolled for Math and 70% enrolled for ...
First of all we add 40 percent that are enrolled for math to 70 percent that are enrolled for economics the answer come 110 percent. 15 percent students enrolled for both subjects then we subtract 110-15 the answer comes 95 percent then percentage means 100 so we subtract 100 percent from 95 percent the answer comes 5 percent so this is the correct answer that is option a) 5 percent
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Community Answer
In a class 40% of the students enrolled for Math and 70% enrolled for ...
To solve this problem, we can use the principle of inclusion-exclusion. Let's break down the problem step by step.
Let's assume the total number of students in the class is 100.
Step 1: Find the number of students enrolled in Math and Economics separately.
- 40% of the students enrolled for Math, so the number of students enrolled in Math = 40% of 100 = 40.
- 70% of the students enrolled for Economics, so the number of students enrolled in Economics = 70% of 100 = 70.
Step 2: Find the number of students enrolled in both Math and Economics.
- 15% of the students enrolled for both Math and Economics, so the number of students enrolled in both = 15% of 100 = 15.
Step 3: Find the number of students who did not enroll in either of the two subjects.
To find this, we need to subtract the number of students enrolled in Math, the number of students enrolled in Economics, and the number of students enrolled in both from the total number of students.
Number of students who did not enroll in either of the two subjects = Total number of students - (Number of students enrolled in Math + Number of students enrolled in Economics - Number of students enrolled in both)
= 100 - (40 + 70 - 15)
= 100 - 55
= 45.
Step 4: Find the percentage of students who did not enroll in either of the two subjects.
To find this, we need to divide the number of students who did not enroll in either of the two subjects by the total number of students and multiply by 100.
Percentage of students who did not enroll in either of the two subjects = (Number of students who did not enroll in either of the two subjects / Total number of students) x 100
= (45 / 100) x 100
= 45%.
Therefore, the correct answer is option A) 5%.
Let's assume the total number of students in the class is 100.
Step 1: Find the number of students enrolled in Math and Economics separately.
- 40% of the students enrolled for Math, so the number of students enrolled in Math = 40% of 100 = 40.
- 70% of the students enrolled for Economics, so the number of students enrolled in Economics = 70% of 100 = 70.
Step 2: Find the number of students enrolled in both Math and Economics.
- 15% of the students enrolled for both Math and Economics, so the number of students enrolled in both = 15% of 100 = 15.
Step 3: Find the number of students who did not enroll in either of the two subjects.
To find this, we need to subtract the number of students enrolled in Math, the number of students enrolled in Economics, and the number of students enrolled in both from the total number of students.
Number of students who did not enroll in either of the two subjects = Total number of students - (Number of students enrolled in Math + Number of students enrolled in Economics - Number of students enrolled in both)
= 100 - (40 + 70 - 15)
= 100 - 55
= 45.
Step 4: Find the percentage of students who did not enroll in either of the two subjects.
To find this, we need to divide the number of students who did not enroll in either of the two subjects by the total number of students and multiply by 100.
Percentage of students who did not enroll in either of the two subjects = (Number of students who did not enroll in either of the two subjects / Total number of students) x 100
= (45 / 100) x 100
= 45%.
Therefore, the correct answer is option A) 5%.
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In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?a)5%b)15%c)0%d)25%Correct answer is option 'A'. Can you explain this answer?
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In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?a)5%b)15%c)0%d)25%Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?a)5%b)15%c)0%d)25%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?a)5%b)15%c)0%d)25%Correct answer is option 'A'. Can you explain this answer?.
In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?a)5%b)15%c)0%d)25%Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?a)5%b)15%c)0%d)25%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enrol for either of the two subjects?a)5%b)15%c)0%d)25%Correct answer is option 'A'. Can you explain this answer?.
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