In an examination, $34\%$ of the candidates fail in Bengali and $42\%$ in English. If $20\%$ fail in Bengali and English, the percentage of those passing in both subjects is:

Let $B$ represent the set of candidates who failed in Bengali, and $E$ represent the set of candidates who failed in English.
From the problem statement:

* $n(B)=34\%$
* $n(E)=42\%$
* $n(B\cap E)=20\%$

Using the set theory principle of union, we can find the total percentage of candidates who failed in at least one of the two subjects:

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

$$n(B\cup E)=34\%+42\%-20\%$$

$$n(B\cup E)=76\%-20\%=56\%$$

The candidates who passed in both subjects are those who did not fail in either subject. Therefore:

$$\text{Percentage passing both subjects}=100\%-n(B\cup E)$$

$$\text{Percentage}=100\%-56\%=44\%$$