In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is: (a) at least 30 (b) at most 20 (c) exactly 25 (d) none of these
ANSWER
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Hint: In this question, we will first find how many numbers of times all newspapers are read, and then find relation between that number and number of times each newspaper is read. Then, we will use this relation to solve the given question.
Complete Step-by-Step solution: We are given that in a college of 300 students, every student reads 5 newspapers. Let us first find out how many times all the newspapers are read. If one student reads 1 newspaper, then the total number of times all newspapers are read = 1. If 300 students read 1 newspaper each, then the total number of times all newspapers are read = $300\times 1=300$. So, if 300 students read 5 newspapers each, then the total number of times all newspapers are read = $300\times 5=1500$. Also, we can write, $\text{Number of times each student read a newspaper}=\dfrac{\text{Total number of times newspapers read}}{\text{Total number of students}}$. Let us now find out the number of newspapers. If each newspaper is read by 1 student, and the total number of times all the newspapers are read is also 1, then we can easily say that the total number of newspapers is one, which one student must have read 1 time. Now, suppose each newspaper is read by 1 student and the total number of times newspapers are read is 300, then the total number of newspapers must also be 300, which 300 different students must have read $\dfrac{300}{300}=1$ time each. Now, suppose each newspaper is read by 2 students and total number of times newspapers are read is 300, then total number of newspapers must $\dfrac{300}{2}=150$, which 300 different students must have read $\dfrac{300}{300}=1$ times each. Now, if each newspaper is read by 60 students and total number of times newspapers are read is 1500, then total number of newspapers must $\dfrac{1500}{60}=25$, which 300 different students must have read $\dfrac{1500}{300}=5$ times each. Therefore, the number of newspapers we get is exactly 25. Hence, the answer is option (c).
Note: If concept is clear to you, then you can directly use the formula: \[\text{Number of newspapers = }\dfrac{\text{Total read time of all the newspapers}}{\text{Total number of times each newspaper is read}}\]. Where, \[\begin{align} & \text{Total read time of all the newspapers} \\ & =\text{ Total number of students }\times \text{ Number of times each student reads a newspaper} \\ \end{align}\].