Calculate the RPI and the required income adjustment given the basket of goods and their prices for two years.

We multiply the weight of each good by its price in Year 1 and sum them up.

$$\text{Total Weighted Price (Year 1)} = (5 \times 100) + (2 \times 200) + (1 \times 50) + (2 \times 600)$$ $$= 500 + 400 + 50 + 1200$$ $$= 2150$$

We multiply the weight of each good by its price in Year 2 and sum them up.

$$\text{Total Weighted Price (Year 2)} = (5 \times 150) + (2 \times 250) + (1 \times 100) + (2 \times 500)$$ $$= 750 + 500 + 100 + 1000$$ $$= 2350$$

The formula for the RPI is:

$$\text{RPI} = \frac{\text{Total Weighted Price (Year 2)}}{\text{Total Weighted Price (Year 1)}} \times 100$$ $$\text{RPI} = \frac{2350}{2150} \times 100$$ $$\text{RPI} \approx 1.093023 \times 100$$ $$\text{RPI} \approx \boxed{\textbf{109.30}}$$

The percentage increase in prices is the RPI minus 100.

$$\text{Inflation Rate} = \text{RPI} - 100$$ $$\text{Inflation Rate} = 109.30 - 100 = 9.30\%$$

To maintain the same living standard, the person's income must increase by the same percentage as the inflation rate.

$$\text{Required Income Increase} = \text{Original Income} \times \frac{\text{Inflation Rate}}{100}$$ $$\text{Required Income Increase} = 10,000 \times \frac{9.3023}{100}$$ $$\text{Required Income Increase} \approx 10,000 \times 0.093023$$ $$\text{Required Income Increase} \approx \boxed{\textbf{930.23}}$$