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In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group?
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In a group of 1st year MBA students 72% like to take coffee 52% like t...
Total Number of Students Calculation
To find the total number of students in the group, let's denote the total number of students as "N".
Step 1: Understanding Preferences
- 72% of students like coffee.
- 52% of students like tea.
- 144 students like both coffee and tea.
Step 2: Using the Formula
We can use the principle of inclusion-exclusion to find the total number of students who like at least one drink.
- Let A be the set of students who like coffee.
- Let B be the set of students who like tea.
The formula for the union of two sets is:
N(A ∪ B) = N(A) + N(B) - N(A ∩ B)
Where:
- N(A ∪ B) is the total number of students who like coffee or tea.
- N(A) = 0.72N (students who like coffee)
- N(B) = 0.52N (students who like tea)
- N(A ∩ B) = 144 (students who like both)
Step 3: Applying Values
Substituting the values into the formula:
N(A ∪ B) = 0.72N + 0.52N - 144
This simplifies to:
N(A ∪ B) = 1.24N - 144
Step 4: Setting Up the Equation
Since N(A ∪ B) cannot exceed the total number of students N, we set:
1.24N - 144 ≤ N
Step 5: Solving for N
Rearranging gives us:
0.24N ≤ 144
So, N ≥ 144 / 0.24
Calculating this gives:
N = 600
Conclusion
The total number of students in the group is 600.
To find the total number of students in the group, let's denote the total number of students as "N".
Step 1: Understanding Preferences
- 72% of students like coffee.
- 52% of students like tea.
- 144 students like both coffee and tea.
Step 2: Using the Formula
We can use the principle of inclusion-exclusion to find the total number of students who like at least one drink.
- Let A be the set of students who like coffee.
- Let B be the set of students who like tea.
The formula for the union of two sets is:
N(A ∪ B) = N(A) + N(B) - N(A ∩ B)
Where:
- N(A ∪ B) is the total number of students who like coffee or tea.
- N(A) = 0.72N (students who like coffee)
- N(B) = 0.52N (students who like tea)
- N(A ∩ B) = 144 (students who like both)
Step 3: Applying Values
Substituting the values into the formula:
N(A ∪ B) = 0.72N + 0.52N - 144
This simplifies to:
N(A ∪ B) = 1.24N - 144
Step 4: Setting Up the Equation
Since N(A ∪ B) cannot exceed the total number of students N, we set:
1.24N - 144 ≤ N
Step 5: Solving for N
Rearranging gives us:
0.24N ≤ 144
So, N ≥ 144 / 0.24
Calculating this gives:
N = 600
Conclusion
The total number of students in the group is 600.
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In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group?
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In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group?.
In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a group of 1st year MBA students 72% like to take coffee 52% like to take tea and 144 students like both the drink what is the total number of students in the group?.
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