Find How Many Speak Hindi and English
Question:
In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find:
(i) how many can speak both Hindi and English
(ii) how many can speak Hindi only
(iii) how many can speak English only
Solution
\[ n(H\cup E)=n(H)+n(E)-n(H\cap E) \] \[ 950=750+460-n(H\cap E) \] \[ 950=1210-n(H\cap E) \] \[ n(H\cap E)=1210-950 \] \[ n(H\cap E)=260 \](i)
\[ \boxed{260} \](ii) Hindi only
\[ n(H)-n(H\cap E) \] \[ =750-260 \] \[ =490 \] \[ \boxed{490} \](iii) English only
\[ n(E)-n(H\cap E) \] \[ =460-260 \] \[ =200 \] \[ \boxed{200} \]