Question

in the group of 240 students 200 opts for history and 90 opts for geography. if the 20 student do not opt for history as well as Geography then how many student opt for both the subject I. e history and geography both? (a) none of thise (b) 170 (c) 40 (D) 70

Answer 1

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Answer 2

Answer:

70

Step-by-step explanation:

We are given that in the group of n(U) = 240 students :

200 opts for history

90 opts for geography.

20 student do not opt for history as well as Geography .

Let n(A) denotes no. of students opts for history

i.e. n(A) = 200

Let n(B) denotes no. of students opts for geography.

i.e. n(B) = 90

Since we are given that 20 student do not opt for history as well as Geography .

⇒n(U)-n(A∪B)=20

⇒240-n(A∪B)=20

⇒220=n(A∪B)

Now we need to calculate student opt for both the subject i.e.n(A∩B)

⇒n(A∪B)= n(A)+n(B)-n(A∩B)

⇒220=200+90 -n(A∩B)

⇒220=290-n(A∩B)

⇒n(A∩B)=290-220

⇒n(A∩B)=70

Hence the number of students opted for both subjects is 70