There are 10 stations on a railway line.The number of different journey tickets that are require by the authorities, is

Question

Arun selected an integer \( x \) between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer \( x \) and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an \( x \) are possible?

Answer 1

With 10 stations, the number of distinct two-station journeys is determined by the combination formula \( \binom{n}{2} \), where \( n \) represents the total station count.

Therefore, the calculation for different journey tickets is as follows:

\[ \binom{10}{2} = \frac{10 \times 9}{2} = 45 \]

This result represents journeys in a single direction. As a ticket covers travel in either direction, we double this value:

\[ 45 \times 2 = 90 \]

Consequently, 90 distinct journey tickets are needed.

There are 10 stations on a railway line.The number of different journey tickets that are require by the authorities, is

The Correct Option is B

Solution and Explanation

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