To determine which two categories have registered the same percentage increase in 2011 compared to 2010, we need to calculate the percentage increase for each expenditure category. The formula for calculating percentage increase is:

$$ \text{Percentage Increase} = \frac{\text{(Expenditure in 2011} - \text{Expenditure in 2010)}}{\text{Expenditure in 2010}} \times 100\% $$

Expenditure Data Table

Let's first organize the given annual expenditure figures for the firm for both years, 2010 and 2011, in a clear table format:

Percentage Increase Calculation for Each Category

Now, we will calculate the percentage increase for each category's expenditure from 2010 to 2011:

• Raw material:
  Expenditure in 2010 = ₹5200
  Expenditure in 2011 = ₹6240
  Increase in expenditure = ₹(6240 - 5200) = ₹1040
  Percentage Increase for Raw material: $$ \frac{1040}{5200} \times 100\% = 20\% $$
• Power & fuel:
  Expenditure in 2010 = ₹7000
  Expenditure in 2011 = ₹9450
  Increase in expenditure = ₹(9450 - 7000) = ₹2450
  Percentage Increase for Power & fuel: $$ \frac{2450}{7000} \times 100\% = 35\% $$
• Salary & wages:
  Expenditure in 2010 = ₹9000
  Expenditure in 2011 = ₹12600
  Increase in expenditure = ₹(12600 - 9000) = ₹3600
  Percentage Increase for Salary & wages: $$ \frac{3600}{9000} \times 100\% = 40\% $$
• Plant & machinery:
  Expenditure in 2010 = ₹20000
  Expenditure in 2011 = ₹25000
  Increase in expenditure = ₹(25000 - 20000) = ₹5000
  Percentage Increase for Plant & machinery: $$ \frac{5000}{20000} \times 100\% = 25\% $$
• Advertising:
  Expenditure in 2010 = ₹15000
  Expenditure in 2011 = ₹19500
  Increase in expenditure = ₹(19500 - 15000) = ₹4500
  Percentage Increase for Advertising: $$ \frac{4500}{15000} \times 100\% = 30\% $$
• Research & Development:
  Expenditure in 2010 = ₹22000
  Expenditure in 2011 = ₹26400
  Increase in expenditure = ₹(26400 - 22000) = ₹4400
  Percentage Increase for Research & Development: $$ \frac{4400}{22000} \times 100\% = 20\% $$

Percentage Increase Summary

Here is a summary of the calculated percentage increases for each expenditure category:

Categories with Same Percentage Increase

From the summary table, we can observe that:

• The expenditure on Raw material increased by 20%.
• The expenditure on Research & Development also increased by 20%.

Both Raw material and Research & Development categories registered the same percentage increase of 20% in 2011 compared to 2010.