In a statistical investigation of 1,003 families of Calcutta, it was found that 63 families had neither a radio nor a T.V, 794 families had a radio and 187 had a T.V. The number of families in that group having both a radio and a T.V is (a) `36` (b)`41` (c) `32` (d) None of these

Options

A. 36
B. 41
C. 32
D. None of these

Answer

B

Explanation

Let R be the set of famulies having a redio and T be the set of families having a TV.
Then
`n (R cup T)`
Number of families having both a radio and a TV .
=1003- 63 = 940
n( R) = 794 and n (T) = 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 Radio = 794 - x
Number of families who have only TV= 187 - x

From Venn diagram
794 - x +x+187 - x = 940
`rArr ` 981- x = 940
`therefore ` x= 981 -940 = 41
Hence the required number of families having boht a redio and a TV is 41 .