a survey was conducted in a group of 100 students of a school. the ratio of students who like mathematics and computer is 3:5. if 30 of them like both subjects and 10 of them like none of them, construct a Venn-diagram to find the number of students who like: a) Mathematics only b) Computer only, and c) at most one subject.
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Answer:
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Given : a survey was conducted in a group of 100 students of a school. the ratio of students who like mathematics and computer is 3:5. if 30 of them like both subjects and 10 of them like none of them,
To Find : number of students who like: a) Mathematics only b) Computer only, and c) at most one subject.
Step-by-step explanation:
Mathematics = 3k
Computer = 5k
30 of them like both subjects
10 of them like none of them
Total = Math + Computer - Both + None
100 = 3k + 5k - 30 + 10
=> 120 = 8k
=> k = 15
Mathematics = 45
Computer = 75
Mathematics only = Mathematics - Both = 45 - 30 = 15
Computer only = Computer - Both =75 - 30 = 45
at most one subject = 100 - Both subjects 100 - 30 = 70
or none + computer only + Mathematics only = 10 + 45 + 15 = 70
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