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
i. Mathematics only ii. computer only iii. at most one subject

"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:  at most one subject.

Solution:

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

70 Students like at most one subject"