Question

In an examination, the number of those who passed to the number of who failed was in the ration of 3:1. Had 8 more students turned up and 6 less passed, the ratio would have been 2:1. Find how many students turned up to the exam.

Answer 1

let p = number of student that passed initially
let f = number of students that failed initially

then we know:\[\frac{p}{f}=\frac{3}{1}\tag{a}\]
now, if 8 more students turned up and 6 less passed, that means the new number that passed must be (p-6) and the new number that failed must be (f+6+8) and we can write:\[\frac{p-6}{f+6+8}=\frac{2}{1}\]therefore:\[\frac{p-6}{f+14}=\frac{2}{1}\tag{b}\]
now you have two equations (a) and (b) and two unknowns p and f, so you should be able to solve to find p and f, and then find the total number of students that turned up to the exam initially (p+f).