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

Let R be the set of families having a radio and T be the set of families having a T.V., 

then $n\left(R\cup T\right)$= The number of families having at least one of the radio and T.V. = 1003 - 63 = 940 

$n\left(R\right)=794\text{ and }n\left(T\right)=187$

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 

$\text{ From Venn diagram, }794-x+x-187-x=940$

Hence, the required number of families having both a radio and a T.V. =41