BITSAT 2024 Shift 1 Paper

In a survey of 1003 families in Calcutta, we have the following information:63 families have neither a radio nor a TV.794 families have a radio.187 families have a TV.We need to calculate how many families have both a radio and a TV.Step-by-step Solution:Calculate the total number of families with either a radio or a TV. Using the formula for the complement set:$n(R \cup T)+n(R \cup T)' = \; \text{ Total families }\;$$n(R \cup T)+63=1003$Solving for $n(R \cup T)$ :$n(R \cup T)=1003-63=940$Apply the principle of inclusion-exclusion from set theory:$n(R \cup T)=n(R)+n(T)-n(R \cap T)$Substitute the known values:$940=794+187-n(R \cap T)$Simplify to find $n(R \cap T)$ :$\;940=981-n(R \cap T)$$\;n(R \cap T)=981-940=41$Therefore, 41 families have both a radio and a TV.