Q45 / 100 · BITSAT 2024 (Memory Based Paper 3) · Mathematics

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a TV, 794 families has a radio and 187 has TV. The number of families in that group having both a radio and a TV is

  • A
    36
  • Correct answer
    B
    41
  • C
    32
  • D
    None of these

Solution

$\begin{aligned} \text { Given, } n(R) & =794 \\ n(T) & =187 \\ n(R \cup T)^{\prime} & =63 \\ n(\mathrm{Total}) & =n(R \cup T)+n(R \cup T)^{\prime} \\ \Rightarrow \quad 1003 & =n(R \cup T)+63 \\ \Rightarrow \quad n(R \cup T) & =940 \end{aligned}$ By set theory $\begin{array}{lc} \Rightarrow & n(R \cup T)=n(R)+n(T)-n(R \cap T) \\ \Rightarrow & 940=794+187-n(R \cap T) \\ \Rightarrow & n(R \cap T)=981-940=41 \end{array}$

Hence, the correct answer is option: 'B'.

Relevant Questions