16)In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice. 125 25 325 225
Question
16)In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice. 125 25 325 225
Solution
To solve this problem, we need to understand that the total number of students is the sum of those who drink apple juice, those who drink orange juice, those who drink both, and those who drink neither.
From the problem, we know that:
- 100 students drink apple juice
- 150 students drink orange juice
- 75 students drink both apple and orange juice
However, the students who drink both juices are being counted twice in the total of 100 + 150. To avoid this, we subtract the 75 students who drink both juices from the total:
100 (apple juice) + 150 (orange juice) - 75 (both) = 175 students
This is the total number of students who drink either apple juice, orange juice, or both.
The problem asks for the number of students who drink neither apple juice nor orange juice. To find this, we subtract the number of students who drink juice from the total number of students:
400 (total students) - 175 (students who drink juice) = 225 students
So, 225 students drink neither apple juice nor orange juice. The correct answer is 225.
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