Question

If $9000$ students appear in two papers in mathematics at a certain examination. Exactly $7400$ and $6600$ students passed in paper A and B respectively. If $6400$ passed in both papers. Find the number of students failed in both papers.

Answer 1

Among $9000$ students,

$7400$ passed in paper $A$.

Among this number there are $6400$ students who passed in paper $B$

Also So there are $(7400-6400)=1000$ students who passed only in paper $A$.

Now come to paper $B$-

$6600$ passed. Again there are $6400$ students who are among the passed in paper $B$ also.

So, ($6600-6400)=200$ students have passed only in paper $B$.
Now, Total passed students $=(6400$ in both papers$+1000$ in only paper $A+200$ only in Paper $B)=7600$ students.

So, failed students in both papers are $(9000-7600)=1400$ students.