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

The correct answer is (b) 120.

Let $x$ be the number of students who appeared for the examination. The ratio of passes to failures was 4:1, so there were $4x$ passes and $x$ failures. If 30 students less had appeared and 20 less passed, the ratio of passes to failures would have been 5:1. This means that there would have been $5(x-20)$ passes and $(x-30)$ failures. We know that $5(x-20) = 4x$, so $x = 120$.

Option (a) is incorrect because 150 is not a factor of 120. Option (c) is incorrect because 100 is not a factor of 120. Option (d) is correct because 120 is a factor of 120.