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

Answer 1

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 one 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 $T.V. = 187 - x$
Now, $794 - x + x + 187 x = 940$
$\Rightarrow 981 - x = 940$ or $x = 981 - 940 = 41$
Hence, the required number of families having both a radio and a $T.V. = 41$