Question

In a survey of 100 students, the number of students studying the various languages was 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: How many students were studying Hindi?

Answer 1

Let us denote, 

Total number of students by n(P) 

Students studying English n(E) 

Students Studying Hindi n(H) 

Students studying Sanskrit n(S) 

According to the question, 

n(P) =100, n(E–H) = 23, n(E ∩ S) =8, n(E) = 26, n(S) = 48, n(H ∩ S) =8, n(E∪H∪S)’=24 

Number of students studying English only = 18 

Now, 

n(E∪H∪S)’=24 

n(P) – n(E∪H∪S) = 24 

100 – 24 = n(E∪H∪S) 

n(E∪H∪S) = 76 n(E∪H∪S) = n(E)+ n(H)+ n(S)– n(E ∩ S)– n(E ∩ H)– n(H ∩ S)+ (E∩ H ∩ S) 

76 = 26+n(H)+48–3–8–8+3 

n(H) = 76–58 

n(H) = 18 

18 Students are studying Hindi.