Question

In a statistical investigation of $1003$ families of Calcutta, it was found that $63$ families has neither a radio nor a $T.V$, $794$ families has a radio and $187$ has $T.V$. The number of families in that group having both a radio and a $T.V$. is

• A. 36
• B. 41
• C. 32
• D. None of these

Answer 1

Answer: (B)

Let $R$ be the set of families having a radio and $T$ the set families having a T.V.,
then $n(R \cup T)=$ The number of families having at least on of the radio and T.V.
$=1003-63=940$
$n(R)=794$ and $n(T)=187$
Let $x$ families have both a radio and a T.V.
Then number of families who have only radio $=794-x$
And the number of families who have only T.V. $=187-x$
From Venn diagram, $794-x+x-187-x=940$
$\Rightarrow 981-x=940$ or $x=981-940=41$
Hence, the required number of families having both a radio and a T.V.
$=41$