This question has an underlying assumption (albeit logical) that all of the people present speak at least one language.

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+1 vote

A gathering of $50$ linguists discovered that $4$ knew Kannada$,$ Telugu and Tamil$,$ $7$ knew only Telugu and Tamil $,$ $5$ knew only Kannada and Tamil $,$ $6$ knew only Telugu and Kannada$.$ If the number of linguists who knew Tamil is $24$ and those who knew Kannada is also $24,$ how many linguists knew only Telugu$?$

- $9$
- $10$
- $11$
- $8$

+3 votes

Best answer

Let $K_a$ denote Kannada, $T_a$ denote Tamil and $T_e$ denote Telegu.

$n(K_a \cup T_a \cup T_e ) = n(K_a) + n(T_a) + n(T_e) - n(K_a \cap T_a ) - n(K_a \cap T_e ) - n(T_e \cap T_a ) + n(K_a \cap T_a \cap T_e )$

$\implies 50 = 24 +24 + n(T_e) - (5+4) - (6+4) - (7+4) + 4$

$\implies 50 = 48 + n(T_e) - 26$

$\implies n(T_e) = 28.$

$\therefore$ Number of people who know Telegu, $n(T_e) =28.$

Number of people who know only Telegu

$= n(T_e) - n(K_a \cap T_e ) - n(T_e \cap T_a ) + n(K_a \cap T_a \cap T_e )$

$= 28 -(6+4) -(7+4) +4$

$= 11$

Correct Option: C.

$n(K_a \cup T_a \cup T_e ) = n(K_a) + n(T_a) + n(T_e) - n(K_a \cap T_a ) - n(K_a \cap T_e ) - n(T_e \cap T_a ) + n(K_a \cap T_a \cap T_e )$

$\implies 50 = 24 +24 + n(T_e) - (5+4) - (6+4) - (7+4) + 4$

$\implies 50 = 48 + n(T_e) - 26$

$\implies n(T_e) = 28.$

$\therefore$ Number of people who know Telegu, $n(T_e) =28.$

Number of people who know only Telegu

$= n(T_e) - n(K_a \cap T_e ) - n(T_e \cap T_a ) + n(K_a \cap T_a \cap T_e )$

$= 28 -(6+4) -(7+4) +4$

$= 11$

Correct Option: C.

+2 votes

+1

Yes i am also getting the same thing...

https://gateoverflow.in/?qa=blob&qa_blobid=12637213641174896015

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