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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 30 more had failed, the ratio of passed to failed candidates would have been 1 : 2, then find the total number of candidates initially?

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 30 more had failed, the ratio of passed to failed candidates would have been 1 : 2, then find the total number of candidates initially? Correct Answer 120

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)/(x + 30) = 1/2

⇒ 10x - 150  = x + 30

⇒ 10x - x = 180

⇒ 9x = 180

⇒ x = 20

∴ Total number of candidates = 20 × 6 = 120

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