An investigation included 100 students to determine the performance of three drinks; milk, tea and coffee. The investigator reported that 10 students take all the three drinks milk, tea and coffee, 20 students take milk and coffee, 25 students take milk and tea, 30 students take coffee and tea. 12 students take milk only, 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of the three drinks is
Question
An investigation included 100 students to determine the performance of three drinks; milk, tea and coffee. The investigator reported that 10 students take all the three drinks milk, tea and coffee, 20 students take milk and coffee, 25 students take milk and tea, 30 students take coffee and tea. 12 students take milk only, 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of the three drinks is
Solution
To find the number of students who did not take any of the three drinks, we first need to find the total number of students who did take at least one drink.
- Students who take all three drinks: 10
- Students who take only milk and coffee: 20 - 10 (since 10 students are already counted in the first category) = 10
- Students who take only milk and tea: 25 - 10 = 15
- Students who take only coffee and tea: 30 - 10 = 20
- Students who take only milk: 12
- Students who take only coffee: 5
- Students who take only tea: 8
Add all these numbers together to find the total number of students who took at least one drink:
10 + 10 + 15 + 20 + 12 + 5 + 8 = 80
Subtract this number from the total number of students (100) to find the number of students who did not take any of the three drinks:
100 - 80 = 20
So, 20 students did not take any of the three drinks.
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