In a certain examination, the number of those who passed was 4 times the number of those who failed. If there had been 35 fewer candidates and 9 more had failed, the ratio of passed and failed candidates would have been 2:1 the total number of candidates was

Let passed students be 4x and failed students be x

Total number of students will be 5x

 If there had been 35 fewer candidates and 9 more had failed, the ratio of passed and failed candidates would have been 2:1

Then, total number of students will be 5x - 35

$$\Rightarrow \frac{(5x - 35) - (x + 9)}{x + 9} = \frac{2}{1}$$

$$\Rightarrow \frac{(4x - 44)}{x + 9} = \frac{2}{1}$$

$$\Rightarrow$$ 4x - 44 = 2x + 18

$$\Rightarrow$$ 2x = 62 (or) x = 31

Total number of students = 5(31) = 155

Hence, option B is the correct answer.