Question

Comprehension

The following questions are based on the information given below:

All the 3200 students of a college in a city know at least one of the three languages ​​English, Telugu and Hindi. 2400 know English, 1700 know Telugu, 800 know Hindi, 1000 know English and Telugu, 500 speak English and Hindi, 300 speak Telugu and Hindi and only 100 know all three languages.

How many know only Hindi?

A. 200

B. 400

C. 100

D. 800

1. B
2. D
3. A
4. C

Answer 1

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.