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 ?

A. $$\frac{{xyz}}{{3\left( {xy + yz + zx} \right)}}$$    km/hr

B. $$\frac{{xyz}}{{\left( {xy + yz + zx} \right)}}$$    km/hr

C. $$\frac{{\left( {xy + yz + zx} \right)}}{{xyz}}$$    km/hr

D. $$\frac{{3xyz}}{{\left( {xy + yz + zx} \right)}}$$    km/hr

Answer: Option D

Solution(By Examveda Team)

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