let

p = the number of passes

f = the number of failures

p + f = the number of the people that appeared at the examination

the ratio of passes to failures was 4:1

P : f = 4 : 1

p = 4f

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

30 less had appeared: p + f - 30

20 less passed: p - 20

number of failures: p + f - 30 - (p - 20) = p + f - 30 - p + 20 = f - 10

the ratio of passes to failures would have been 5:1

(p - 20) : (f - 10) = 5 : 1

p - 20 = 5(f - 10)

by solving the system of equations

p = 4f

p - 20 = 5(f - 10)

we find

p = 120 passes

f = 30 failures

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p + f = 150

150 students appeared for the examination.