Question

45% of the students of a Padampur Shiksha Niketan School play basketball, 40% play cricket and 30% play both. If 360 students play neither basketball nor cricket, use Venn-diagram and find the number of students in the school. Also, find the number of students who play only basketball. Ans: 800, 120​

Answer 1

Let's use a Venn diagram to solve the problem. Let B represent the set of students who play basketball, C represent the set of students who play cricket, and n(B ∩ C) represent the number of students who play both.

Then we have:

n(B) = 45% of the total number of students
n(C) = 40% of the total number of students
n(B ∩ C) = 30% of the total number of students
n(Not B and Not C) = 360 students
We want to find the total number of students, which is given by the formula:

n(Total) = n(B) + n(C) - n(B ∩ C) + n(Not B and Not C)

Substituting the given values, we get:

n(Total) = 45% + 40% - 30% + 360
n(Total) = 55% + 360
n(Total) = 800

Therefore, the total number of students in the school is 800.

To find the number of students who play only basketball, we can use the formula:

n(B only) = n(B) - n(B ∩ C)

Substituting the given values, we get:

n(B only) = 45% - 30%
n(B only) = 15%

Since 15% of 800 is 120, we can conclude that 120 students play only basketball.