# Percentage Problem 14

### From Homeworkwiki

**In a examination Richard secured 37% marks and failed by 18 marks. In the same examination,**

**Mark secured 42 % marks and got 12 marks more than the minimum pass marks. Calculate the maximum marks**

**and the pass per cent of the marks in the examination.**

**Solution:** Let the maximum marks be x

In the case of Richard : Pass marks = 37 % of x + 18

And, in the case of Mark : Pass marks = 42 % of x - 12

But pass marks for an examination are the same for both

=> 37 % of x + 18 = 42 % of x - 12

=> 18 + 12 = 42 % of x - 37 % of x

=> 30 = 5 % of x

and, 5 / 100 X x = 30

=> x = 30 X 100 / 5 = 600

i.e. max marks for the examination = 600

N0w, pass marks = 37 % of 600 + 18

= 37 / 100 X 600 + 18 = 240

=> Pass percent of the marks = 240 / 600 X 100 % = 40 %