There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 45% play football, how many play both ?

$$\eqalign{ & n\left( A \right) = \left( {\frac{{75}}{{100}} \times 600} \right) = 450 \cr & n\left( B \right) = \left( {\frac{{45}}{{100}} \times 600} \right) = 270 \cr & \therefore n\left( {A \cap B} \right) \cr} $$
$$ = n\left( A \right) + n\left( B \right) - n\left( {A \cup B} \right)$$     $$n\left( {A \cup B} \right)$$   $$ -\, 600$$
$$\eqalign{ & = \left( {450 + 270 - 600} \right) \cr & = 120 \cr} $$