A man goes on trek from the bottom to the top of a mountain. He starts at $6$ am of $15$ th October, $2017$ from the bottom and reaches the top at $6$ pm of the same day. On $16$ th October, $2017$ he starts from the top at $6$ am and goes back following exactly the same route and reaches the bottom at $6$ pm. Based on the given situation, the following possibilities are to be analysed.
I. It is not possible to find a point on the route which he will cross at the same time each day.
II. It is possible to find a point on the route which he will cross at the same time each day provided only if the travels on each day with equal uniform speed.
III. It is always possible to find a point on the route which he will cross at the same time each day irrespective of his speed of travel.

Only I is true

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Only II is true

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Only III is true

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Both I and II are true

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Solution

The correct option is B Only II is true
We can analyze this problem as covering a distance at uniform distance in a certain period of time.
And then coming back the same distance at the same time.
This is possible if the speed is constant and he will cross a certain point at the same time.
Thus. It is possible to find a point on the route which he will cross at the same time each day provided only if he travels on each day with equal uniform speed.
Hence, Option B is correct.

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