In an examination, 41% of students failed in Economics, 35% of students failed in Geography and 39% of students failed in History, 5% of students failed in all the three subjects, 14% of students failed in Economics and Geography, 21% of students failed in Geography and History and 18% of students failed in History and Economics. Find the percentage of students who failed in only Economics.

Correct option is B

Given:

41% of students failed in Economics.
35% of students failed in Geography.
39% of students failed in History.
5% of students failed in all three subjects.
14% of students failed in both Economics and Geography.
21% of students failed in both Geography and History.
18% of students failed in both History and Economics.
Solution:

Let the total percentage of students be 100%.
The formula for the number of students who failed in Economics alone is:
Only Economic = Economics – (Economics and Geography) + (Economics and History) – (All three subjects)


Only Economics = $$41\% - \left(14\% + 18\% - 5\%\right)$$​​

Only Economics= $$41\% - \left(32\% - 5\%\right) = 41\% - 27\%$$​=14%


Thus, the percentage of students who failed in only Economics is: 14%