question_answer

in statistical survey of 1003 families of Kolkata, it was found that 63 families has neither a radio nor a TV. 794 families has a radio and 187 has TV. The number of families in that group having both a radio and a TV is ________.

A) 40

B) 41

C) 42

D) 43

Correct Answer: B

Solution :

[41] Let R be the set of families having a radio and T be the set of families having a TV. Then \[n(R\cup T)\]=Number of families having at least one of the radio and TV =1003-63=940 n (R)=794 and n(T)=187 Let x be the number of families having both a radio and a TV. Then number of families who have only radio=794-x Number of families who have only TV=187-x From venn diagram, 794-x+x+187-x=940 \[\Rightarrow \]981-x=940 \[\therefore \]x=981-940=41 Hence, the required number of families having both a radio and a TV is 41.