In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The total number of newspapers are:

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The answer is 25.

A little thought provoking, but not at all tough. Perhaps you had problem in visualizing the situation. So, forget about all the intricacies of Set Theory, set aside mathematical complexities and let me explain to you in a more simple, logical and practical way.

First of all, ask all 300 students to stand in a row, one beside the other, each carrying the 5 different newspapers he/she reads. Okay?
So now, 300 students are carrying a total of (300 x 5) = 1500 copies (may not all unique) of newspapers.
Great!

Now, assume that you know the names of the newspapers.
Take a microphone, and announce the name of a particular newspaper. Call the students carrying that specific newspaper, and order them to submit it to you.
Put all the copies you get, in a box.
Clearly, each time you announce a newspaper, you'll get 60 copies of that newspaper submitted to you (since each one is read by 60 students).
Thus each box will contain 60 copies of a particular newspaper. Right?

If this process is continued, eventually after some time you'll have all the 1500 copies submitted to you.

Now, it goes without saying, that the number of boxes = the number of unique newspapers.
If each box contains 60 copies, and there are total 1500 copies, then clearly there are (1500/60) = 25 boxes

Hence the result.

Hope you understand.