Question:
Let \(n > 2\) be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :
Let \(n > 2\) be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :
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Total tracks \(\binom n2\); blue tracks are the n sides of the polygon; red = \(\binom n2-n\).
Updated On: Nov 5, 2026
- 201
- 199
- 101
- 200
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The Correct Option is A
Solution and Explanation
Total straight tracks \(=\binom n2=\frac{n(n-1)}{2}\). Nearest-station pairs (adjacent on the circle) \(= n\) blue lines.
Red lines \(=\frac{n(n-1)}{2}-n=\frac{n(n-3)}{2}\).
Given red \(=99\times\) blue: \(\frac{n(n-3)}{2}=99n\Rightarrow n-3=198\Rightarrow n=201\).
Answer: (1) 201
Red lines \(=\frac{n(n-1)}{2}-n=\frac{n(n-3)}{2}\).
Given red \(=99\times\) blue: \(\frac{n(n-3)}{2}=99n\Rightarrow n-3=198\Rightarrow n=201\).
Answer: (1) 201
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