Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

To solve this problem, we first need to understand the relationship between speed, distance, and time. The formula is Distance = Speed x Time.

1. First, let's find the distance to point A. We know that if Robert travels at 10 kmph, he will reach at 2 P.M. If he starts at 12 noon, that means he travels for 2 hours. So, the distance to point A is 10 kmph x 2 hours = 20 km.

2. Now, we know that if he travels at 15 kmph, he will reach at 12 noon. That means he travels for 1 hour. But we already know the distance is 20 km. So, if he travels at 15 kmph for 1 hour, he will only cover 15 km. That means he must have started his journey 1 hour before noon, at 11 A.M.

3. Now, we want him to reach at 1 P.M. That means he has 2 hours to travel from 11 A.M. to 1 P.M. We already know the distance is 20 km.

4. So, to find the speed he needs to travel at, we use the formula Speed = Distance / Time. That gives us Speed = 20 km / 2 hours = 10 kmph.

So, Robert must travel at 10 kmph to reach point A at 1 P.M.