Question

In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only ?

• A. 275
• B. 300
• C. 325
• D. 350

Answer 1

Answer: (B)

300

Answer 2

Total number of students = 500 Let H be the set showing number of students who can speak Hindi = 475 and B be the set showing number of students who can speak Bengali = 200 So, n (H) = 475 and n (B) = 200 and given that n (B $\cup$ H) = 500 we have n (B $\cup$ H) = n (B) + n (H) - n (B $\cap$ H) $\Rightarrow$ 500 = 200 + 475 - n (B $\cap$ H) so, n (B $\cup$ H) = 175 Hence, persons who speak Hindi only = n (H) - n $\cap$ H) = 475 - 175 = 300