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There are 21 persons and there are three languages - French German and Japanese. 10 persons speak German, 12 persons speak Japanese, and 10 persons speak French. 4 can speak only French and 5 can speak only Japanese. 4 can speak French as well as German. 3 persons can speak all languages. How many persons speak Japanese and German?

There are 21 persons and there are three languages - French German and Japanese. 10 persons speak German, 12 persons speak Japanese, and 10 persons speak French. 4 can speak only French and 5 can speak only Japanese. 4 can speak French as well as German. 3 persons can speak all languages. How many persons speak Japanese and German? Correct Answer 5

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Given

Number of person = 21

Number of persons speak German = 10

Number of persons speak Japanese = 12

Number of persons speak French = 10

Calculation

Let number of person speak French, German and Japanese represents by F, G and J.

French persons = a + b + c + g =  10

Japanese persons = b + d + g + e = 12

German = c + g + e + f = 10

Persons speak all languages, g = 3

persons speak only French, a = 4

Persons speak only Japanese, d = 5

Person speak French and German, (c + g) = 4

c + 3 = 4

⇒ c = 4 - 3

⇒ c = 1

a + b + c + g =,10

⇒ 4 + b + 1 + 3 = 10

⇒ b = 10 - 8

⇒ b = 2

b + d + g + e = 12

⇒ 2 + 5 + 3 + e =12

⇒ e = 12 - 10

⇒ e = 2

persons speak Japanese and German, (g + e) = 3 + 2

⇒ 5

∴ 5 persons speak Japanese and German.

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