According to the average speed formula,

P=$\frac{1}{4}$, Q=$\frac{3}{5}$, R=$\frac{3}{20}$

X= 8 km/hr, Y= 6km/hr, Z=10 km/hr

∴ Required average speed 

$$\begin{gathered} =\frac{1}{{\displaystyle \frac{\mathrm{P}}{\mathrm{X}}}+{\displaystyle \frac{\mathrm{Q}}{\mathrm{Y}}}+{\displaystyle \frac{\mathrm{R}}{\mathrm{Z}}}} \\ =\frac{1}{{\displaystyle \frac{1}{4\times 8}}+{\displaystyle \frac{3}{5\times 6}}+{\displaystyle \frac{3}{20\times 10}}} \\ =\frac{1}{{\displaystyle \frac{1}{32}}+{\displaystyle \frac{1}{10}}+{\displaystyle \frac{3}{200}}} \\ =\frac{1}{{\displaystyle \frac{25+80+12}{800}}}=\frac{800}{117} \\ =6.83 \mathrm{km}/\mathrm{hr} \end{gathered}$$

Hence, Option A is correct.