Find Students Studying Hindi and English-Hindi
Question:
In a survey of 100 students, the number of students studying the various languages were found to be:
English only = 18, English but not Hindi = 23, English and Sanskrit = 8, English = 26, Sanskrit = 48, Sanskrit and Hindi = 8, No language = 24.
Find:
(i) How many students were studying Hindi?
(ii) How many students were studying English and Hindi?
Solution
\[ n(E)=26 \] \[ n(E-H)=23 \] \[ n(E\cap H)=26-23 \] \[ =3 \](ii)
\[ \boxed{n(E\cap H)=3} \]Students studying at least one language:
\[ 100-24=76 \] \[ n(E\cup S\cup H)=76 \] \[ 76=26+48+n(H)-8-8-3 \] \[ 76=55+n(H) \] \[ n(H)=21 \](i)
\[ \boxed{n(H)=21} \]