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In an examination 70% candidates passed in prelims and 55% candidates passed in Mains. If 62% candidates passed in both these subjects, then what per cent of candidates failed in both the exams?Options37%43%15%26%

Question

In an examination 70% candidates passed in prelims and 55% candidates passed in Mains. If 62% candidates passed in both these subjects, then what per cent of candidates failed in both the exams?Options37%43%15%26%

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Solution

To solve this problem, we need to understand that the percentage of candidates who passed both exams is included in the percentage of candidates who passed each individual exam.

Here's the step-by-step solution:

  1. Start by adding the percentage of candidates who passed the prelims (70%) and the percentage of candidates who passed the mains (55%). This gives us 125%.

  2. However, the candidates who passed both exams have been counted twice in this total. So, we need to subtract the percentage of candidates who passed both exams (62%) from our total. This gives us 125% - 62% = 63%.

  3. The percentage we have now (63%) represents the candidates who passed at least one of the exams. To find the percentage of candidates who failed both exams, we subtract this from 100%.

So, 100% - 63% = 37%.

Therefore, 37% of candidates failed in both the exams.

This problem has been solved

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