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

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)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let R be the set of families having a radio and T the set families having a T. V., then n (R ∪ 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 ⇒ 981 - x = 940 or x = 981 - 940 = 41 Hence, the required number of families having both a radio and a T.V. = 41

Q. 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

Q. 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