- Home
- Standard 11
- Mathematics
1.Set Theory
easy
In a group of $400$ people, $250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?
A
$50$
B
$50$
C
$50$
D
$50$
Solution
Let $H$ be the set of people who speak Hindi, and E be the set of people who speak English
$\therefore n(H \cup E)=400, n(H)=250, n(E)=200$
$n(H \cap E)=?$
We know that:
$n(H \cup E)=n(H)+n( E )-n(H \cap E)$
$\therefore 400=250+200-n(H \cap E)$
$\Rightarrow 400=450-n(H \cap E)$
$\Rightarrow n(H \cap E)=450-400$
$\therefore n(H \cap E)=50$
Thus, $50$ people can speak both Hindi and English.
Standard 11
Mathematics
Similar Questions
medium