Correct Answer - Option 4 : C

Given:

Total student = 3200

Numbers of student know English, n(E) = 2400

Numbers of student know Telugu, n(T) = 1700

Numbers of student know Hindi, n(H) = 800

Numbers of student know both English and Telugu, n(E ∩ T) = 1000

Numbers of student know both English and Hindi, n(H ∩ E) = 500

Numbers of student know both Hindi and Telugu, n(H ∩ T) = 300

Numbers of student know all three languages, n(E ∩ H ∩ T) = 100

Formula used:

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)

Where,

(A ∪ B) → Total A and B

(A) → Total A

(B) → Total B

(C) → Total C

(A ∩ B) → Total common part of A and B

(A ∩ C) → Total common part of A and C

(C ∩ B) → Total common part of C and B

(A ∩ B ∩ C) → Total common part of A, B and C.

Calculation:

Number of student Know only Hindi = n(H) − n(H ∩ E − n(H ∩ T) + n(A ∩ B ∩ C)

⇒ The required student = 800 − 500 − 300 + 100 = 100

∴ Number of student Know only Hindi is 100.