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**Hint:**Let the total number of students be \[100\]

Let A be the set of students who failed in Hindi

So $35\% {\text{ of 100}} = 35$

So $n(A) = 35$

Similarly let B be the set of students who failed in English

$n(B) = 45\% {\text{ of 100}} = 45$

And also we know that $20\% $ failed in both

So $n(A \cap B) = 20\% {\text{ of 100}} = 20$

We know that $n(A \cup B) = n(A) + n(B) - n(A \cap B)$

**Complete step by step solution:**

Here in this question, we are given that in an examination, $35\% $ of the total students failed in Hindi and $45\% $ failed in English and $20\% $ failed in both. So firstly we need to assume the total number of students in the examination. Let us assume that the total number of students be \[100\]

Total students who failed in Hindi$ = 35\% {\text{ of 100}} = \dfrac{{35}}{{100}} \times 100 = 35$

Now we also know that $45\% $ failed in English$ = 45\% {\text{ of 100}} = \dfrac{{45}}{{100}} \times 100 = 45$

And we know that $20\% $ of the students failed in both the subjects so number of students who failed in both the subjects$ = 20\% {\text{ of 100}} = 20$

Let A be the set of students who failed in Hindi

So $35\% {\text{ of 100}} = \dfrac{{35}}{{100}} \times 100 = 35$

So $n(A) = 35$

Similarly let B be the set of students who failed in English

$n(B) = 45\% {\text{ of 100}} = \dfrac{{45}}{{100}} \times 100 = 45$

Also let that $A \cap B$ be the total students who failed in both the subjects.

And also we know that $20\% $ failed in both

So $n(A \cap B) = 20\% {\text{ of 100}} = 20$

Now we need to find the percentage of the students who passed in both the subjects which is given by =${\text{total students }} - {\text{ n(A}} \cup {\text{B)}}$

Now as we know that

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$

Putting the values of $n(A),n(B),n(A \cap B)$ we get

$n(A \cup B) = 35 + 45 - 20 = 60$

Here the $n(A \cup B)$ represents the total students who failed in Hindi and English.

And $n(A \cap B)$ represents the students who failed in both the subjects.

So the total students passing in Hindi and English$ = 100 - n(A \cup B)$

$ = 100 - 60 = 40$

Now for percentage, $\dfrac{{{\text{number of students}}}}{{{\text{total students}}}} \times 100$

$ = \dfrac{{40}}{{100}} \times 100 = 40\% $

**Note:**We can do it this way as it is given that $35\% $ of the total students failed in Hindi and $45\% $ failed in English and $20\% $ failed in both. It means that $(35 - 20)\% = 15\% $failed exclusively in Hindi and $(45 - 20)\% = 25\% $ exclusively in English. So total $\% $ failed in Hindi, English and Both are

$15\% + 25\% + 20\% = 60\% $

So the students passed in both subjects$ = (100 - 60)\% = 40\% $

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