P scored 30% marks and failed by 30 marks, Q scored 40% marks and obtained 40 marks more than those required to pass. The pass percentage is:

Let us assume the total amount of marks is X. 

If P scores 30% of the marks, P will score 0.3X. And we are told that this is 30 marks less than the passing marks. 
So, Passing marks will be 0.3X+30.

And at the same time, we are told that with 40% of the marks, Q got 40 more marks than the passing marks. 
So, Passing marks will be 0.4X-40

Equating the two equations, we get X = 700. 

Passing marks will be 240. 

The percentage required to pass will be 240/700. Which is 12/35 or 34.28%.