Answer

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**Hint**: The question is of the concept of time, speed and distance. We have to find the speed when a person goes and comes a specific amount of distance in a given time. First we will find the distance, then since we are given the time taken by the person we will use the formula of speed to find the speed of the person in the given situation. The formula is given by,

$ Speed = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}} $

This formula gives the speed, do note that the unit of the speed will depend on what is the unit of time and the distance.

**Complete step by step solution:**

The distance covered by the person will be the twice of the given distance because he goes a distance of $ 10km $ and then comes back, so the effective distance of the person is,

$ \Rightarrow 10 \times 2 $

$ \Rightarrow 20 $

Thus he travels a distance of $ 20 $ km, the time is given as $ 2\dfrac{1}{2} $ hours , this can be written as proper fraction in the form of $ \dfrac{5}{2} $ hours, now we will use the formula for speed,

$ Speed = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}} $

Upon applying the formula we get,

$ \Rightarrow speed = \dfrac{{20}}{{\dfrac{5}{2}}} $

$ \Rightarrow speed = \dfrac{{20 \times 2}}{5} $

Solving which we get,

$ \Rightarrow speed = 4 \times 2 $

$ speed = 8\dfrac{{km}}{{hr}} $

Thus the speed of the person will be \[8km.h{r^{ - 1}}\].

**So, the correct answer is “ \[8km.h{r^{ - 1}}\]”.**

**Note**: The question if it had asked us to find the time when other two are given, or the distance when the other two parameters are given the answer would have been found with the help of the formulas given below,

$ {\text{Distance = Speed}} \times {\text{Time}} $

$ Time = \dfrac{{{\text{Distance}}}}{{{\text{Speed}}}} $ ,

Again remember that the units will depend on the unit of the input parameters.

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