Total Students Calculation
This problem involves calculating the total number of students using provided percentages for sports participation and the count of non-participants.
Student Participation Percentages
The given data is:
- Only Cricket: 30%
- Only Football: 20%
- Only Basketball: 10%
- Both Football & Cricket (Intersection): 20%
- Both Basketball & Cricket (Intersection): 15%
- Both Football & Basketball (Intersection): 10%
- All Three Games: 5%
- No Games: 15 students
Players Percentage Sum
We calculate the sum of percentages for distinct groups playing at least one game:
- Only Cricket: 30%
- Only Football: 20%
- Only Basketball: 10%
- Cricket and Football only (excluding all three): $20\% - 5\% = 15\%$
- Basketball and Cricket only (excluding all three): $15\% - 5\% = 10\%$
- Football and Basketball only (excluding all three): $10\% - 5\% = 5\%$
- All Three Games: 5%
Total percentage of students playing at least one game = $30\% + 20\% + 10\% + 15\% + 10\% + 5\% + 5\% = 95\%$
Non-Players Percentage
The percentage of students playing no games is calculated as:
$100\% - (\text{Percentage playing at least one game}) = 100\% - 95\% = 5\%$
Final Total Students
We are given that 15 students play no games. This 15 corresponds to the 5% calculated above.
Let '$T$' represent the total number of students.
The equation is:
$ 5\% \times T = 15 $
Converting percentage to a fraction:
$ \frac{5}{100} \times T = 15 $
Solving for '$T$':
$ T = 15 \times \frac{100}{5} $
$ T = 15 \times 20 $
$ T = 300 $
Thus, the total number of students is 300.
Important Questions from Set Theory and Venn Diagram (Notes)
A student is free to choose only Chemistry, only Biology or both. If out of $32$ students, Chemistry has been chosen by $16$ and Biology by $25$, then how many students have chosen Biology but not Chemistry?
- Fourteen of the students in a class are girls. Eight students in the class wear blue shirts. Two are neither girls nor wear blue shirts. Five students who wear blue shirts are girls. How many students are there in the class?
- In a group of 44 players, 26 play hockey, 24 play football and 24 play cricket. Eight of them play both hockey and football, 12 play both football and cricket, and 5 play all the three games. How many play both hockey and cricket?
- Which of the following statements are true ?
A. Set A = {x : x $\in$ R and 2 < x < 3} is a null set.
B. Set A = {x : x $\in$ R and 2 < x < 4} is a singleton set.
C. Set A = {x : x $\in$ R and 1 < x < 9} is an infinite set.
D. Set A = {x : x $\in$ R and 1 < x < 9} is a finite set.
E. Set A = {a, b, c, d, e} and B = {c, d, a, e, b} are equal sets.
Choose the correct answer from the options given below : - Suppose three meetings of a group of professors were arranged in Mumbai, Delhi and Chennai. Each professor of the group attended exactly two meetings. 21 professors attended Mumbai meeting, 27 attended Delhi meeting and 30 attended Chennai meeting. How many of them attended both the Chennai and Delhi meetings?
