In an examination, the number of those who passed was 5 times the number of those who failed. If there had been 75 less passed candidates and 10 more had failed, the ratio of passed to failed candidates would have been 1 : 2, then find the total number of candidates initially?
Let the number of failed candidates = x
Number of passed candidates = 5x
Total number of candidates = 5x + x = 6x
According to the question
(5x - 75 - 10)/(x + 10 + 75) = 1/2
⇒ 10x - 150 - 20 = x + 10 + 75
⇒ 10x - x = 255
⇒ 9x = 255
⇒ x = 85/3
∴ Total number of candidates = 85/3 × 6 = 170