The correct option is B 20≤α≤320
Let H be the set of people who speaks Hindi,
and E be the set of people who speaks English.
n(U)=800,n(H)=500,n(E)=320
n(H∩E)=α
n(H∪E)=n(H)+n(E)−n(H∩E)
⇒n(H∪E)=820−α
⇒α=820−n(H∪E)
For α to be minimum, n(H∪E) should be maximum.
αmin=820−800=20
Also, α≤min{n(H),n(E)}=320
Hence, 20≤α≤320