Club Members Activity Analysis
The problem asks for the fraction of members who like exactly one activity (either swimming or cycling) out of the total members in a club.
Calculating Members for Each Activity
First, determine the number of members who like only swimming and only cycling.
- Total members: $N = 300$
- Members who like swimming: $S = 160$
- Members who like cycling: $C = 140$
- Members who like both swimming and cycling: $S \cap C = 60$
Calculate the number of members who like only swimming:
$ S_{only} = S - (S \cap C) = 160 - 60 = 100 $
Calculate the number of members who like only cycling:
$ C_{only} = C - (S \cap C) = 140 - 60 = 80 $
Determining Total Members Liking Exactly One Activity
The total number of members who like exactly one activity is the sum of those who like only swimming and those who like only cycling.
$ N_{exactly\_one} = S_{only} + C_{only} = 100 + 80 = 180 $
Finding the Required Fraction
To find the fraction of total members who like exactly one activity, divide the number of members who like exactly one activity by the total number of members.
$ \text{Fraction} = \frac{N_{exactly\_one}}{N} $
Substitute the calculated values:
$ \text{Fraction} = \frac{180}{300} $
Simplify the fraction:
$ \frac{180}{300} = \frac{18 \times 10}{30 \times 10} = \frac{18}{30} = \frac{6 \times 3}{6 \times 5} = \frac{3}{5} $
Therefore, the fraction of total members who like exactly one activity is $\frac{3}{5}$.
Important Questions from Venn Diagram Problems
In a group of 110 students, 23 students did not participate in any of the two games: Badminton and Chess. 45 students participated in Badminton and 61 students participated in Chess. How many students participated in Badminton only?
In a class of 100 students, every student has passed in one or more of the three subjects, i.e History, Economics and English. Among all the student, 24 students have passed in English only, 14 students have passed in History only 11 students have passed in both English and Economics only, and 12 students have passed in both English and History only. A total of 50 students have passed in History. If only 5 students have passed in all three subjects, then how many students have passed in Economies only?
60 students participated in one or more of the three competitions, i. e. Quiz, Extempore and Debate. A total of 22 students participated either in Quiz only or in Extempore only. 4 students participated in all three competitions. A total of 14 students participated in any of the two competitions only. How many students participated in Debated only?
In a class of 75 students, 40 students participate in Cricket, 28 students participate in Hockey, and 12 students participate in both Cricket and Hockey, whereas 19 students do not participate in any of the two sports. How many students participate only in Hockey?
How many students like french?
A. 30
B. 35
C. 40
D. 45
