# 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?

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(EHS)’=24

Number of students studying English only = 18

Now,

n(EHS)’=24

n(P) – n(EHS) = 24

100 – 24 = n(EHS)

n(EHS) = 76

n(EHS) = 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.

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