Question

In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only?

• A. Number of people speaking English only = 37
  
• B. Number of people speaking English only = 47
  
• C. Number of people speaking English only = 57
  
• D. Number of people speaking English only = 67
  

Answer 1

The correct option is C Number of people speaking English only = 57


Let A be the set of people who speak English.

B be the set of people who speak French.

A - B be the set of people who speak English and not French.

B - A be the set of people who speak French and not English.

A ∩ B be the set of people who speak both French and English.

Given,

n(A) = 72 n(B) = 43 n(A ∪ B) = 100

Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)

= 72 + 43 - 100

= 115 - 100

= 15

Therefore, Number of persons who speak both French and English = 15

n(A) = n(A - B) + n(A ∩ B)

⇒ n(A - B) = n(A) - n(A ∩ B)

= 72 - 15

= 57

Therefore, Number of people speaking English only = 57