In an examination $35\%$ students fail in Mathematics, $15\%$ fail in English. If $10\%$ fail in both, the pass percentage is:

Let's apply the principle of inclusion-exclusion for sets to find the total percentage of students who failed in at least one subject.
Let:

* $M$ be the percentage of students failing in Mathematics = $35\%$
* $E$ be the percentage of students failing in English = $15\%$
* $M\cap E$ be the percentage of students failing in both subjects = $10\%$

The total percentage of students who failed ($M\cup E$) is:

$$\text{Total Fail}\%=M+E-(M\cap E)$$

$$\text{Total Fail}\%=35\%+15\%-10\%=40\%$$

The percentage of students who passed all subjects is the complement of the total fail percentage:

$$\text{Pass}\%=100\%-\text{Total Fail}\%=100\%-40\%=60\%$$