In a group in a group of 500 students, there are 475 students who can speak Hindi and 200 speak Bengali. What is the number of students who can speak Hindi only ?
A.
275
B.
300
C.
325
D.
350
Answer :
300
Solution :
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, $$n\left( H \right) = 475$$ and $$n\left( B \right) = 200$$ and given that $$n\left( {B \cup H} \right) = 500$$
we have
$$\eqalign{
& n\left( {B \cup H} \right) = n\left( B \right) + n\left( H \right) - n\left( {B \cap H} \right) \cr
& \Rightarrow \,500 = 200 + 475 - n\left( {B \cap H} \right) \cr
& {\text{So, }}n\left( {B \cap H} \right) = 175 \cr} $$
Hence, persons who speak Hindi only $$ = n\left( H \right) - n\left( {B \cap H} \right) = 475 - 175 = 300$$
Releted MCQ Question on Calculus >> Sets and Relations
Releted Question 1
If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.