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.

Question: 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.

Solution:

Now,
e = 5%
b + e = 14%
⇒ b = 9%

and, d + e = 18%
⇒ d = 13%
Therefore, Percentage of students who failed only in Economics = a = 41% - (b + e + d)
⇒ a = 41% - (9 + 5 + 13)%
⇒ a = 41% - 27%
⇒ a = 14%
Hence, 14% is the correct answer.