In a test, 40% of the students failed in English, 30% failed in Hindi and 15% failed in both subjects. If 360 students passed in both subjects, how many students took the test?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 800
A student who passed in both subjects is one who failed in neither. First find the per cent who failed in at least one subject: those who failed in both are counted in both failure figures, so they are subtracted once.
Failed in at least one subject \(=40\%+30\%-15\%=55\%\)
Passed in both subjects \(=100\%-55\%=45\%\)
\(45\%\) of the students \(=360\)
Students \(=\displaystyle\frac{360\times 100}{45}=800\)
Checking the other options
Option (1): 1200 — Incorrect. This takes 40% + 30% = 70% as failing in at least one subject, forgetting that the 15% who failed in both are counted twice; then 360 is wrongly taken as 30%.
Option (2): 2400 — Incorrect. This adds the 15% who failed in both instead of subtracting it, so 360 is wrongly taken as 15%.
Option (4): 600 — Incorrect. This uses only English: 360 is taken as the 60% who passed in English, but some of them failed in Hindi.