An international conference is attended
by 65 people. They all speak at least one
of English, French and German
language. Suppose 15 speak English
and French, 13 speak English and
German, 12 speak French and German
and 5 speak all the three languages. A
total of 30 people can speak German
and 30 can speak French. What is the
number of people who can speak only
English?
(a) 17
(b) 20
(c) 22
(d) 40
Answers
Given : international conference is attended by 65 people.
They all speak at least one of English, French and German language.
15 speak English and French, 13 speak English and German, 12 speak French and German and 5 speak all the three languages. A total of 30 people can speak German and 30 can speak French.
To Find : What is the number of people who can speak only English?
(a) 17
(b) 20
(c) 22
(d) 40
Solution:
Total T = 65
speak German G = 30
speak French F = 30
speak English = E
speak English and French, E ∩ F = 15
speak English and German, E ∩ G = 13
speak French and German, F ∩ G = 12
speak all the three languages. E ∩ F ∩ G = 5
Speak None = 0 as They all speak at least one of English, French and German language.
T = G + F + E - E ∩ F - E ∩ G -F ∩ G + E ∩ F ∩ G + None
=> 65 = 30 + 30 + E - 15 - 13 - 12 + 5 + 0
=> 65 = 25 + E
=> E = 40
40 Speak English
people who can speak only English
= E - E ∩ F - E ∩ G + E ∩ F ∩ G
= 40 - 15 - 13 + 5
= 17
17 can speak only English
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