Problem: In an examination 60% of the candidates passed in Hindi, 70% passed in English and 25% failed in both. Find the overall pass percentage?

Solution:
To find the overall pass percentage, we need to first find the percentage of candidates who passed in both Hindi and English.

Step 1: Calculate the percentage of candidates who passed in both Hindi and English.

Let the percentage of candidates who passed in both Hindi and English be x%.

Total candidates = 100% (let this be represented as T)

Given, 25% failed in both Hindi and English. Therefore, (100 - 25)% = 75% of the candidates passed either in Hindi or English or both.

60% passed in Hindi. Therefore, (100 - 60)% = 40% did not pass in Hindi.

70% passed in English. Therefore, (100 - 70)% = 30% did not pass in English.

Using the formula for the union of two sets, we can write:

Total candidates who passed in Hindi or English or both = Candidates who passed in Hindi + Candidates who passed in English - Candidates who passed in both Hindi and English

= 60% + 70% - x%

= 130% - x%

Total candidates who failed in Hindi and English = 100% - Total candidates who passed in Hindi or English or both

= 100% - (130% - x%)

= x% - 30%

Given, 25% failed in both Hindi and English. Therefore, x% - 30% = 25%

=> x% = 55%

Therefore, 55% of the candidates passed in both Hindi and English.

Step 2: Calculate the overall pass percentage.

Total candidates = 100%

Given, 25% failed in both Hindi and English. Therefore, the percentage of candidates who passed in at least one of the subjects = 100% - 25% = 75%

Therefore, the overall pass percentage = Percentage of candidates who passed in at least one of the subjects = 75%

Conclusion: The overall pass percentage is 75%.