Question

In a school there are 100 students 60 of them don't like chocolate and 50 don't like biscuit and 10 of them like none them how many of them like both??​

Answer 1

SOLUTION

GIVEN

In a school there are 100 students 60 of them don't like chocolate and 50 don't like biscuit and 10 of them like none them

TO DETERMINE

The number of students like both

EVALUATION

Let C and B denotes the set of students who like chocolate and biscuits respectively

Also U denotes the set of all students

Now it is given that in a school there are 100 students 60 of them don't like chocolate and 50 don't like biscuit and 10 of them like none them

n(U) = 100

n(C') = 60

n(B') = 50

n(C' ∩ B') = 10

We have to find ,

The number of students like both

= n(C ∩ B) = ?

Now n(C') = 60 gives

n(C) = 100 - 60 = 40

Again n(B') = 50 gives

n(B) = 100 - 50 = 50

n(C' ∩ B') = 10 gives

n((C ∪ B) ') = 10

⇒ n(U) - n(C ∪ B) = 10

⇒ n(C ∪ B) = 100 - 10

⇒ n(C ∪ B) = 90

Again we know that

n(C ∪ B) = n(C) + n(B) - n(C ∩ B)

⇒ 90 = 40 + 50 - n(C ∩ B)

⇒ n(C ∩ B) = 90 - 90

⇒ n(C ∩ B) = 0

Hence the number of students like both = 0

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