Question

In a committee, $50$ people speak Hindi, $20$ speak English and $10$ speak both Hindi and English. How many speak at least one of these two languages?

Answer 1

Calculate the number of people speaking at least two languages.

Let $n\left(H\right)$ be the number of people speaking Hindi, $n\left(E\right)$ be the number of people speaking English and $n\left(H\cap E\right)$ speak both English and Hindi.

Given,

$$\begin{gathered} n\left(H\right)=50 \\ n\left(E\right)=20 \\ n\left(H\cap E\right)=10 \end{gathered}$$

So, number of people speaking at least one of the two languages $=n\left(H\cup E\right)$.

$\begin{array}{rcl}n\left(H\cup E\right)& =& n\left(H\right)+n\left(E\right)-n\left(H\cap E\right)\\ & =& 50+20-10\\ & =& 60\end{array}$

Hence, the number of people speaking at least one of the two languages is $60$.