31. In a group of 400 people in USA, 250 can speak Spanish and 200 can speak English. How many people can speak both Spanish and English?

Question

31. In a group of 400 people in USA, 250 can speak Spanish and 200 can speak English. How many people can speak both Spanish and English?
60
80
50
40​

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Skylar 3 days 2021-09-13T22:53:11+00:00 1 Answer 0 views 0

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    2021-09-13T22:54:13+00:00

    Step-by-step explanation:

    ANSWER

    Let H be the set of people who speak Hindi, and E be the set of people who speak English

    ∴n(H∪E)=400,n(H)=250,n(E)=200

    n(H∩E)=?

    We know that:

    n(H∪E)=n(H)+n(E)−n(H∩E)

    ∴400=250+200−n(H∩E)

    ⇒400=450−n(H∩E)

    ⇒n(H∩E)=450−400

    ∴n(H∩E)=50

    Thus, 50 people can speak both Hindi and English.

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