A candidate scoring x% marks in an examination fails by 'a' marks while another candidate who scores y% marks, gets 'b' marks more than the minimum required pass marks. What is the maximum marks for the examination ?

Let the maximum total marks be M. Let the passing marks be P. 

Candidate scoring x% marks fails by 'a' marks. This means that he score 'a' marks less than the passing marks.

$$\dfrac{x}{100}\times M=P-a\rightarrow1$$

Candidate scoring y% marks fails gets 'b' marks more than the passing marks. 

$$\dfrac{y}{100}\times M=P+b\rightarrow2$$

Subtracting eq. 1 from eq. 2 -

$$\dfrac{y-x}{100}\times M=b+a$$

$$M=\dfrac{100\left(b+a\right)}{\left(y-x\right)}$$