Question

In a village there are 60 families. Out of these 28 families speak only Tamil and 20 families speak only Urdu. How many families speak both Tamil and Urdu.

Answer 1

Let, the number of families who speak Tamil only $=n\left(T\right)=28$

The number of families who speak Urdu only $=n\left(U\right)=20$

The number of families who speak both Tamil and Urdu $=n(T\cap U)$

The number of total families $=n(T\cup U)=60$

A.T.Q,

$n(T\cup U)=n(T\cap U)+n\left(T\right)+n\left(U\right)$

$⟹60=n(T\cap U)+28+20$

$⟹n(T\cap U)=60-48=12$

$\therefore 12$ families speak both Tamil and Urdu.