Answer

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**Hint:**We can solve the problem by using the general relations and using the Venn diagram.

We will apply the formula of \[n(H \cup E) = n(H) + n(E) + n(H \cap E)\]. Here, \[H\] means number of students who can speak Hindi and \[E\] means the number of students who can speak English.

Then, using the formula and given information we can find the number of students who can speak both.

**Complete step by step answer:**

It is given that; the total number of students in the class is \[45\].

The number of students who can speak Hindi is \[22\].

The number of students who can speak English is \[12\].

We have to find the number of students who can speak both Hindi and English.

So, as per the given information

\[n(H \cup E) = 45\]

\[n(H) = 22\]

\[n(E) = 12\]

Let us consider the number of students who can speak both Hindi and English is \[x\] that is \[n(H \cap E) = x\].

We have to find the value of \[n(H \cap E)\].

We know that,

\[ \Rightarrow n(H \cup E) = n(H) + n(E) + n(H \cap E)\]

Substitute the values in the above formula we get,

\[ \Rightarrow 45 = 22 + 12 + x\]

Simplifying we get,

\[ \Rightarrow x = 11\]

Hence, the number of students who can speak both Hindi and English is \[11\].

**$\therefore $ The correct answer is option A) \[11\]**

**Note:**

We can solve the sum by using a Venn diagram.

Here, the red shaded part indicates the number of students who can speak Hindi is \[22\].

The blue shaded part indicates the number of students who can speak English is \[12\].

The green shaded part indicates the number of students who can speak both Hindi and English.

The total number of students in the class is \[45\].

We have to find the value of the green shaded part.

So, the value of green-shaded part is

\[45 - (22 + 12) = 11\]

Hence, the number of students who can speak both Hindi and English is \[11\].

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