In a committee, 50 people speak Hindi, 20 speak English and 10 speak both Hindi and English. How many speak at least one of these two languages?

Given:


People who speak Hindi = 50


People who speak English = 20


People who speak both English and Hindi = 10


To Find: People who speak at least one of these two languages


Let us consider,


People who speak Hindi = n(H) = 50


People who speak English = n(E) = 20


People who speak both Hindi and English = n(H E) = 10


People who speak at least one of the two languages = n(H E)


Venn diagram:



Now, we know that,


n(A B) = n(A) + n(B) – n(A B)


Therefore,


n(H E) = n(H) + n(E) – n(H E)


= 50 + 20 – 10


= 60


Thus, People who speak at least one of the two languages are 60.


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