In an examination, the ratio of passes to failures was 4 : 1. Had 30 less appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1. How many students appeared for the examination?

Given,

Ratio of Passes to Failures = 4 : 1

Let students who Pass = 4k and Fail = k

Total students appeared for examination = 4k + k = 5k

Given,

30 students didn't appear for examination.

Now total students appeared for exam = 5k − 30

If 20 less students passed the exam, then students that pass the exam now = 4k − 20

Number of students that fail in exam = (5k − 30) − (4k − 20) = k − 10.

The new ratio of passes to failures = 5 : 1

$\therefore \dfrac{4k - 20}{k - 10} = \dfrac{5}{1} \\[1em] \Rightarrow 4k - 20 = 5(k - 10) \\[1em] \Rightarrow 4k - 20 = 5k - 50 \\[1em] \Rightarrow -20 + 50 = 5k - 4k \\[1em] \Rightarrow k = 30.$

Total students who appeared exam = 5k = 5(30) = 150.

Hence, total number of students appeared for the examination = 150.