In an examination, 35% of total students failed in Hindi, 45% failed in…

Use the inclusion–exclusion principle to find the percent who failed at least one subject, then subtract from 100% to get those who passed both.

Method 1 (inclusion–exclusion): failed at least one = failed in Hindi + failed in English − failed in both

• failed at least one = 35% + 45% − 20% = 60%

• passed both = 100% − 60% = 40%

Method 2 (count only-fail categories):

• only failed Hindi = 35% − 20% = 15%

• only failed English = 45% − 20% = 25%

• failed both = 20%

• total failed = 15% + 25% + 20% = 60%, so passed both = 100% − 60% = 40%

Answer: 40% of the students passed in both subjects.