Let $x$ be the maximum marks in the examination.
Therefore, Peter got $30\%$ of $x$
And Paul got $40\%$ of $x$
In terms of the maximum marks Paul got $0.4x-0.3x = 0.1x$ more than Peter. --------(1)
The problem however, states that Paul got 15 marks more than the passing mark and Peter got 10 marks less than the passing mark.
Therefore, Paul has got 15 + 10 = 25 marks more than Peter.-------- (2)
Equating (1) and (2), we get
$x$ is the maximum mark and is equal to 250 marks.
We know that Peter got $30\%$ of the maximum marks.
Therefore, Peter got
We also know that Peter got 10 marks less than the passing mark.
Therefore, the passing mark will be 10 marks more than what Peter got = $75 + 10 = 85$
Edit: For a shortcut alternative method, check comment by Chirag Goyal.