A man's annual income increases by Rs 1.2 lakhs, but the income tax rate on his income reduces from 12% to 10%. Even after these changes, the amount of tax he pays every year remains exactly the same as before. What is his new increased annual income in rupees lakhs?

Introduction / Context:
This question involves percentage changes applied to income and tax rates. It checks whether you can set up an equation that keeps the tax amount constant while both the income and the tax rate change. Such problems are common in aptitude tests related to percentage applications and income tax scenarios.

Given Data / Assumptions:

• Original annual income = x lakhs (unknown).
• Original tax rate = 12 percent.
• New annual income = x + 1.2 lakhs.
• New tax rate = 10 percent.
• Tax amount paid before and after the change is the same.
• We assume only the rate and income change; no extra deductions are involved.

Concept / Approach:
Tax paid is calculated as: Tax = Income * Tax rate. We equate the old tax and the new tax because the question states that the tax amount remains unchanged. This gives an equation in x. After solving for x, we add 1.2 to get the new income and then compare it with the options given in rupees lakhs.

Step-by-Step Solution:
Step 1: Let original income be x lakhs. Step 2: Original tax = 12 percent of x = 0.12 * x. Step 3: New income = x + 1.2 lakhs. Step 4: New tax = 10 percent of new income = 0.10 * (x + 1.2). Step 5: Since tax amount is unchanged, set 0.12 * x = 0.10 * (x + 1.2). Step 6: Expand right side: 0.12x = 0.10x + 0.12. Step 7: Subtract 0.10x from both sides to get 0.02x = 0.12. Step 8: Solve for x: x = 0.12 / 0.02 = 6 lakhs. Step 9: New income = x + 1.2 = 6 + 1.2 = 7.2 lakhs.

Verification / Alternative check:
Original income = 6 lakhs, original tax at 12 percent = 0.12 * 6 = 0.72 lakhs. New income = 7.2 lakhs, new tax at 10 percent = 0.10 * 7.2 = 0.72 lakhs. The tax amount is 0.72 lakhs in both cases, which confirms that the condition of equal tax is satisfied and validates the calculation.

Why Other Options Are Wrong:
6: This is the original income rather than the new increased income. 8.4: At this income, tax at 10 percent would be 0.84 lakhs, which is greater than the original tax. 9.6: This would further increase the tax well above the original amount. 10.2: This also leads to a higher tax and does not satisfy the condition of equal tax amounts.

Common Pitfalls:
Some students subtract percentages directly or confuse percentage change in income with percentage change in tax. Another mistake is to assume that a lower tax rate always means less tax, forgetting that the income may have increased. Always write the explicit expressions for tax before and after the change and then equate them to form a correct equation.

Final Answer:
The increased annual income of the man is 7.2 lakhs.