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. Find the number of students who appeared for the examination.

Given,

Ratio of passes to failures = 4 : 1

Let no. of students passed be 4x and failed be x.

So, total students who appeared for examination (originally) = 5x (4x + x)

Given,

Had 30 less appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1.

So, now students appeared = 5x - 30 and no. of students passed = 4x - 20

No. of students failed = (5x - 30) - (4x - 20) = 5x - 4x - 30 + 20 = x - 10.

Now ratio = 5 : 1.

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

No. of students who appeared for examination originally = 5x = 5 x 30 = 150.

Hence, no. of students who appeared for examination are 150.