A person travels three equal distance at a speed of x km/hr, y km/hr and z km/hr respectively. What is the average speed for the whole journey ?

Answer: Option D

Let each distance be equal to d
Then, total distance travelled = 3d
Total time taken :
$$\begin{array}{rl}& =\left(\frac{d}{x}+\frac{d}{y}+\frac{d}{z}\right)\text{hr}\\ & =\frac{d\left(xy+yz+zx\right)}{xyz}\text{ hr}\end{array}$$
∴ Average speed :
$$\begin{array}{rl}& =\left[3d\times \frac{xyz}{d\left(xy+yz+zx\right)}\right]\text{km/hr}\\ & =\frac{3xyz}{\left(xy+yz+zx\right)}\text{ km/hr}\end{array}$$