Question

In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is

(a) 10

(b) 9

(c) 5

(d) 4

Answer 1

Correct option is (b) 9

n(A U B) = n(A) + n(B) - n(A ꓵ B)

Total no. of people = 15

No. of people who neither read French nor English = 3

No. of people who read at least one language = 15 - 3 = 12 = n(A U B)

No. of people who can read French = 7 = n(A)

No. of people who can read English = 8 = n(B)

n(A ꓵ b) is no. of people who speak both languages

Therefore,

12 = 7 + 8 - n(A ꓵ b)

n(A ꓵ b) = 3

Therefore, no. of people who speak both languages = 3

No. of people who read only French = 7 - 3 = 4

No. of people who read only English = 8 - 3 = 5

No. of people who read exactly one language = 4 + 5 = 9

Hence, 9 is the correct answer.