In an examination $75\%$ passed in Maths, $80\%$ passed in Bengali, $65\%$ in both and $45$ students failed in both subjects. Then the number of students appeared are:

Let $M$ represent the percentage of students who passed in Maths, and $B$ represent the percentage of students who passed in Bengali.
Given parameters:

* $n(M)=75\%$
* $n(B)=80\%$
* $n(M\cap B)=65\%$

Let's compute the total percentage of students who passed in at least one subject:

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

$$n(M\cup B)=75\%+80\%-65\%$$

$$n(M\cup B)=155\%-65\%=90\%$$

Therefore, the percentage of students who failed in both subjects is:

$$\text{Percentage failed}=100\%-90\%=10\%$$

We are told that $45$ students failed in both subjects. Let the total number of students be $x$:

$$10\%\text{ of }x=45$$

$$\frac{10}{100}\times x=45$$

$$x=45\times 10=450$$

Since $450$ is not listed in options A, B, or C, the correct choice is Option D.