In a group of 800 people, 550 can speak Hindi and 450 can speak English. How many can speak both Hindi and English?

Solution: People who can speak Hindi $,n\left(A\right)=550$
People who can speak English$,n\left(B\right)=450$
Total number of person in the group $n\left(A\cup B\right)=800$
$\therefore$ People who can speak both hindi and english,
$n\left(A\cap B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cup B\right)=550+450-800=200.$