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 I87 has TV. The number of families in that group having both a radio and a TV is

Let R be the set of families having a radio and Z be the set of families having a TV.

Then,

$\mathrm{n}(\mathrm{R}\cup \mathrm{T})$

= Number of families having at least one of the radio and TV

= 1003 - 63 = 940

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

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,

$794-\mathrm{x}+\mathrm{x}+187-\mathrm{x}=940$

$\Rightarrow 981-x=940$

$\therefore \mathrm{x}=981-940=41$

Hence, the required number of families having both a radio and a TV is 41.