Percentage evaulation Queestion from GRE

Question

A question from GRE book says:

A candidate who gets 30 percent marks in an examination fails by 30 marks,but another candidate who gets 42 percent marks get 42 more marks than necessary for passing.Find the maximum number of marks and total necessary for passing.

I started with it by : Let passing marks =x Then for Student1; (x-30) Student 2;(x+42) But what should i equate it to get them compared and find 'x' and then total marks.

Answer 1

Let Maximum marks be $x$, and Passing marks $y$

Then according to first condition $$x\times \frac{30}{100}=y-30\tag{1}$$

According to second condition $$x\times \frac{42}{100}=y+42\tag{2}$$ Solving $(1)$ & $(2)$ yields $$x=600, y=210$$

So, Maximum marks $=600$, Marks requied for passing$=210$

Answer 2

Hint: First find the number of points that corresponds to $1\%$.