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

Question

Infinity Learn · Accepted Answer

Let R be the set of families having a radio and Z be the set of families having a TV.Then,$$n(R$$∪$$T)=$$ Number of families having at least one of the radio and $$TV=$$ $$1003$$ $$-$$ $$63$$ $$=$$ $$940n(R)=794$$ and $$n(T)=187Let$$ x be the number of families having both a radio and a TV.Then number of families who have only Radio $$=$$ $$794$$ $$-$$ xNumber of families who have only TV $$=$$ $$187$$ $$-$$ xFrom Venn diagram,$$794$$−$$x+x+187$$−$$x=940$$⇒ $$981$$−$$x=940$$∴ $$x=981$$−$$940=41Hence$$, the required number of families having both a radio and a TV is $$41$$.

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

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