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?
17
20
22
40
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2018
– Total people |E U F U G| = 65 (since all speak at least one language).
– We are given: |E ∩ F| = 15, |E ∩ G| = 13, |F ∩ G| = 12, |E ∩ F ∩ G| = 5.
– We are also given: |G| = 30, |F| = 30.
– We can find the number of people speaking exactly two languages:
– |E ∩ F only| = |E ∩ F| – |E ∩ F ∩ G| = 15 – 5 = 10
– |E ∩ G only| = |E ∩ G| – |E ∩ F ∩ G| = 13 – 5 = 8
– |F ∩ G only| = |F ∩ G| – |E ∩ F ∩ G| = 12 – 5 = 7
– We can find the number of people speaking only one language using the given total for F and G:
– |G| = |G only| + |E ∩ G only| + |F ∩ G only| + |E ∩ F ∩ G|
30 = |G only| + 8 + 7 + 5 => 30 = |G only| + 20 => |G only| = 10.
– |F| = |F only| + |E ∩ F only| + |F ∩ G only| + |E ∩ F ∩ G|
30 = |F only| + 10 + 7 + 5 => 30 = |F only| + 22 => |F only| = 8.
– The total number of people is the sum of those speaking only one language, exactly two languages, and all three:
– |E U F U G| = |E only| + |F only| + |G only| + |E ∩ F only| + |E ∩ G only| + |F ∩ G only| + |E ∩ F ∩ G|
– 65 = |E only| + 8 + 10 + 10 + 8 + 7 + 5
– 65 = |E only| + 48
– |E only| = 65 – 48 = 17.