2023
Mathematics
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In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.
A.
750
B.
850
C.
250
D.
150
Correct Answer: 250
Explanation
Let F be the set of people who can speak French and E be the set of people who can speak English. Then, n(F) = 400 n(E) = 350 n(F ∪ E) = 500 We have to find n(F ∩ E). Now, n(F ∪ E) = n(F) + n(E) – n(F ∩ E) ⇒ 500 = 400 + 350 – n(F ∩ E) ⇒ n(F ∩ E) = 750 – 500 = 250. ∴ 250 people can speak both languages.
Let F be the set of people who can speak French and E be the set of people who can speak English. Then, n(F) = 400 n(E) = 350 n(F ∪ E) = 500 We have to find n(F ∩ E). Now, n(F ∪ E) = n(F) + n(E) – n(F ∩ E) ⇒ 500 = 400 + 350 – n(F ∩ E) ⇒ n(F ∩ E) = 750 – 500 = 250. ∴ 250 people can speak both languages.THIS WEEK's
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