A taxpayer's annual income increases from Rs 10 lakhs per year to Rs 11 lakhs per year, and over the same range the income tax paid rises from Rs 80,000 to Rs 92,500. Based on this change, what is the marginal tax rate on the additional income?

Introduction / Context:
This question focuses on the concept of the marginal tax rate in the context of a progressive income tax system. In most modern tax systems, higher levels of income are taxed at higher rates, and the marginal tax rate measures the tax on each additional rupee of income earned. Understanding how to compute the marginal tax rate from changes in income and tax paid is important for both exam preparation and real life financial planning.

Given Data / Assumptions:

• Initial income: Rs 10 lakhs per year.
• New income: Rs 11 lakhs per year.
• Initial tax paid: Rs 80,000 per year.
• New tax paid: Rs 92,500 per year.
• Marginal tax rate is defined as the change in tax divided by the change in income, expressed as a percentage.

Concept / Approach:
The marginal tax rate answers the question, "What percentage of the next rupee earned is paid in tax?" It is computed using the formula: marginal tax rate = (change in tax liability / change in taxable income) * 100. This is different from the average tax rate, which is total tax divided by total income. In a progressive system, the marginal tax rate on additional income is usually higher than the average tax rate because additional income may fall in a higher tax slab.

Step-by-Step Solution:
Step 1: Compute the change in income. Change in income = New income − Initial income = Rs 11,00,000 − Rs 10,00,000 = Rs 1,00,000. Step 2: Compute the change in tax paid. Change in tax = New tax − Initial tax = Rs 92,500 − Rs 80,000 = Rs 12,500. Step 3: Use the marginal tax rate formula. Marginal tax rate = (Change in tax / Change in income) * 100. Step 4: Substitute values: (12,500 / 1,00,000) * 100 = 0.125 * 100 = 12.5 percent. Step 5: Match this value with the closest option given in the question.

Verification / Alternative check:
To verify, consider that an increase of Rs 1,00,000 in income produced an extra tax liability of Rs 12,500. If the marginal tax rate were 10 percent, the change in tax would be only Rs 10,000, which is too low. If it were 15 percent, the change would be Rs 15,000, which is too high. Therefore, only Rs 12,500 fits, which corresponds exactly to 12.5 percent. This confirms that the marginal tax rate is 12.5 percent of the additional income.

Why Other Options Are Wrong:
Option B, 8 percent, would give a tax change of only Rs 8,000 on an extra Rs 1,00,000 of income, which does not match the actual change of Rs 12,500. Option C, 10 percent, would lead to a tax change of Rs 10,000 and is still too low. Option D, 15 percent, implies a tax increase of Rs 15,000, which is greater than the given difference. Only option A, 12.50 percent, matches the actual data precisely.

Common Pitfalls:
A typical mistake is to confuse marginal and average tax rates and to divide total tax by total income instead of using the change in tax and the change in income. Another error is to miscalculate the differences, especially when dealing with large numbers like lakhs, and to forget to convert fractions into percentages. Careful use of the formula and stepwise calculation avoids these mistakes.

Final Answer:
The marginal tax rate on the additional income is 12.50%.