Question

In a school there are 200 students. 100 play cricket, 50 play hockey and 60 play basketball.30 students play both cricket and hockey, and 35 play both hockey and basketball. 45 play both basketball and cricket. Find Out:- a.)What is the maximum number of students who play at least one game? b.)What is the maximum number of students who play all the three games? c.)What is the minimum number of students playing atleast one game? d.)What is the number of student playing all the three games?

Answer 1

HEY DEAR . ✌

_______________________


The maximum no of students playing one game is 100.
The maximum no of students playing all 3 games is 110.
The least no of students who play one game is 50.
d)110

HOPE , IT HELPS .
FOLLOW ME .✌

Answer 2

Answer:

a) The maximum number of students who play at least one game - 130

b) The maximum number of students who play all the three games - 30

c) The minimum number of students playing atleast one game - 120

d) The number of student playing all the three games -20

Step-by-step explanation:

Given : In a school there are 200 students. 100 play cricket, 50 play hockey and 60 play basketball. 30 students play both cricket and hockey, and 35 play both hockey and basketball. 45 play both basketball and cricket.

To find : a)What is the maximum number of students who play at least one game?

b)What is the maximum number of students who play all the three games?

c)What is the minimum number of students playing atleast one game?

d)What is the number of student playing all the three games?

Solution :

Consider the Venn diagram attached below in which we convert all the values in term of x.

Since the number of student cannot be negative.

So, $x-20\geq 0$

For the minimum number of students playing all the three games is x=20.

For maximum value of x,

$30-x\geq 0$

i.e.  $x\leq 30$

If x is more than 30, 30-x has negative value which is not possible.

So, maximum value of x is 30.

Now, Total number of students playing at least one game is

$=100+x-15+35-x+x-20$

$=100+x$

We know, For minimum number x=20

The minimum number of students playing at least one game is 100+20=120

For maximum number x=30

The maximum number of students playing at least one game is 100+30=130