In proximate analysis, when a $10 \mathrm{~kg}$ moisture-free solid sample is heated in a furnace at $950^{\circ} \mathrm{C}$ in the absence of air, its mass is reduced by $6 \mathrm{~kg}$. If the same $10 \mathrm{~kg}$ moisture-free solid sample is heated in the furnace at the same temperature in the presence of air, its mass is reduced by $7 \mathrm{~kg}$. The percentage of fixed carbon in the sample is___________.
- $20\%$
- $60\%$
- $10\%$
- $30\%$
