In a college of 300 students every...

MathematicsTypes of Sets and Set OperationsJEE Advanced 1998Easy

View in:English Hindi

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:C

Visualized Solution (English)

Understanding the Scenario

Total Students = $300$
Newspapers read by each student = $5$
Students reading each newspaper = $60$
Let the number of newspapers be $n$

The Concept of Double Counting

Concept: Double Counting Principle
Total Reading Events (from Students) = Total Reading Events (from Newspapers)

Calculating Total Readings (Students)

Total Readings = (Number of Students) $\times$ (Newspapers per Student)
Total Readings = $300 \times 5$

Total Readings Result

Total Readings = $1500$

Calculating Total Readings (Newspapers)

Total Readings = (Number of Newspapers) $\times$ (Students per Newspaper)
Total Readings = $n \times 60$

Setting up the Equation

Equating both expressions:
$60 n = 1500$

Solving for .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } n

$n = \frac{1500}{60}$
$n = 25$

Final Conclusion

Final Answer: Exactly 25
Key Takeaway: Double counting ensures consistency in set interactions.
Verification: $25 \times 60 = 1500$ and $300 \times 5 = 1500$ .

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