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In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is?
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In a class of 100 students, 73 like coffee, 80 like tea and 52 like le...
Understanding the Problem
In a class of 100 students, we have the following preferences:
- 73 students like coffee
- 80 students like tea
- 52 students like lemonade
We need to determine the maximum and minimum number of students who like all three drinks.
Calculating Maximum Students Liking All Three Drinks
To find the maximum number of students who can like all three drinks, we consider the smallest group:
- The smallest group is lemonade, with 52 students.
Thus, the maximum number of students who like all three drinks is 52.
Calculating Minimum Students Liking All Three Drinks
For the minimum, we can use the principle of inclusion-exclusion:
- Total liking at least one drink = 73 (coffee) + 80 (tea) + 52 (lemonade) - x (students liking all three).
- Where x is the number of students liking all three drinks.
Let’s denote the number of students who don't like any drink as 'y'. Then we have:
- 100 = Total students = students liking at least one drink + y
From the above:
- 100 = 73 + 80 + 52 - x + y
- Rearranging gives: y = x - 105
To ensure y is non-negative, we must have x ≥ 105. Hence, the minimum number of students who like all three drinks is 0.
Final Calculation of Difference
Now, the difference between the maximum and minimum number of students who like all three drinks is:
- Maximum = 52
- Minimum = 0
Difference = 52 - 0 = 52
Thus, the answer is 52.
In a class of 100 students, we have the following preferences:
- 73 students like coffee
- 80 students like tea
- 52 students like lemonade
We need to determine the maximum and minimum number of students who like all three drinks.
Calculating Maximum Students Liking All Three Drinks
To find the maximum number of students who can like all three drinks, we consider the smallest group:
- The smallest group is lemonade, with 52 students.
Thus, the maximum number of students who like all three drinks is 52.
Calculating Minimum Students Liking All Three Drinks
For the minimum, we can use the principle of inclusion-exclusion:
- Total liking at least one drink = 73 (coffee) + 80 (tea) + 52 (lemonade) - x (students liking all three).
- Where x is the number of students liking all three drinks.
Let’s denote the number of students who don't like any drink as 'y'. Then we have:
- 100 = Total students = students liking at least one drink + y
From the above:
- 100 = 73 + 80 + 52 - x + y
- Rearranging gives: y = x - 105
To ensure y is non-negative, we must have x ≥ 105. Hence, the minimum number of students who like all three drinks is 0.
Final Calculation of Difference
Now, the difference between the maximum and minimum number of students who like all three drinks is:
- Maximum = 52
- Minimum = 0
Difference = 52 - 0 = 52
Thus, the answer is 52.
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In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is?
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In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is? 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 of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is?.
In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is? 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 of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is?.
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