Question

half of the students of a class like to play cricket 1/4 of the remaining likes to play football, remaining 24 students to play badminton finfd the total no. of students

Answer 1

Here, let A be the set of students who likes to play cricket and B be the set of students who likes to play football.

As per question: n(A∪B)=35

n(A)=24

n(A∩B)=5

We know, n(A∪B)=n(A)+n(B)−n(A∩B)

⇒n(B)=n(A∪B)−n(A)+n(A∩B)

=35−24+5

=16

Hence number of students who like to play football =16.

Answer 2

The total number of students is 64.

Given: One-half of the students of a class like to play cricket, 1/4th of the remaining likes to play football, and the remaining 24 students like to play badminton.

To Find: The total number of students.

Solution:

Let the total number of students be 'x'.

The fraction of students who like to play cricket = 1 / 2

The number of students who like to play cricket = x / 2

Remaining number of students = x - x/2

                                                    = x / 2

The number of students who like to play football = ( 1 / 4 ) × ( x / 2 )

                                                                                  = x / 8

Remaining number of students = ( x / 2 ) - ( x / 8 )

                                                   = 3x / 8

So, the number of students who like to play football = 3x / 8

It is said that the remaining 24 students like to play badminton. So, we can frame an equation from the above-given information;

              3x / 8 = 24

          ⇒  x  = ( 24 × 8 ) / 3

          ⇒  x  = ( 8 × 8 )

                   = 64

Hence, the total number of students is 64.

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