Question

In a group of 950 persons, 750 can speak in Hindi and 460 can speak in English. Find how many speak Hindi only.

Answer 1

For solving this problem we assume that the total number of persons as set $'\mu '$ and persons who speak Hindi as $'A'$ and the persons who speak English as $'B'$. The number of persons who are speaking Hindi only is calculated by $A-\left( A\cap B \right)$. We know the value of $'A'$ but for finding the value of $\left( A\cap B \right)$ we use the relation $\mu =A+B-\left( A\cap B \right)$.

Complete step by step answer:
Let us assume that total number of persons present as
$\mu =950$
Let us assume that the persons who speak Hindi as $'A'$, so we can take
$A=750$
Let us assume that the persons who speak English as $'B'$, so we can take
$B=460$
We know that the relation of $'\mu ,A,B'$ is
$\mu =A+B-\left( A\cap B \right)$
Now, by substituting the values of $'\mu ,A,B'$ in above equation we get

& \Rightarrow 950=750+460-\left( A\cap B \right) \\\ & \Rightarrow \left( A\cap B \right)=1210-950 \\\ & \Rightarrow \left( A\cap B \right)=260 \\\ \end{aligned}$$ Now, let us assume that the number of persons who speak Hindi only as $$'x'$$. We know that the number of persons who speak Hindi is given as $$x=A-\left( A\cap B \right)$$ By substituting the required values in above equation we get $$\begin{aligned} & \Rightarrow x=750-260 \\\ & \Rightarrow x=490 \\\ \end{aligned}$$ **Therefore, we can say that there are 490 people who speak Hindi only.** **Note:** This problem can be solved in another method. Let us assume that total number of persons present as $$\mu =950$$ Let us assume that the persons who speak Hindi as $$'A'$$, so we can take $$A=750$$ Let us assume that the persons who speak English as $$'B'$$, so we can take $$B=460$$ Now, let us assume that the number of persons who speak Hindi only as $$'x'$$. We know that the number of persons who speak Hindi is given as $$x=A-\left( A\cap B \right)$$ We know that the relation of $$'\mu ,A,B'$$ is $$\mu =A+B-\left( A\cap B \right)$$ The above equation is modified as $$\Rightarrow A-\left( A\cap B \right)=\mu -B$$ By substituting the required values in above equation we get $$\begin{aligned} & \Rightarrow x=950-460 \\\ & \Rightarrow x=490 \\\ \end{aligned}$$ Therefore, we can say that there are 490 people who speak Hindi only.