In an examination, 65% of the students passed in History and 55% passed in Hindi. If 5% of the students failed in both subjects, what percentage of the students passed in both subjects?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 25%
Leaving out the 5% who failed in both, the rest passed in at least one subject. Adding the two pass percentages counts those who passed in both twice, so the excess over that total is the overlap.
Passed in at least one subject \(=100\%-5\%=95\%\)
Passed in both \(=65\%+55\%-95\%=25\%\)
Only History \(=65\%-25\%=40\%\); only Hindi \(=55\%-25\%=30\%\)
25% of the students passed in both subjects.
Why the other options are incorrect
Option (1) 30% — Incorrect. This is the share who passed in Hindi only.
Option (2) 35% — Incorrect. This is the share who failed in History (\(100\%-65\%\)).
Option (3) 20% — Incorrect. It would leave 45% + 35% + 20% + 5% \(=105\%\), more than all the students.