Mr. X, a businessman had the income in the year 2010, such that he earned a profit of 20% on his investment in the business. In the year 2011, his investment was less by ₹ 5000 but still had the same income (Income = Investment + Profit) as that in 2010. Thus, the percent profit earned in 2011 increased by 6%. What was his investment in 2010?

### Concept & Equation The problem explicitly defines the relationship: $$Income = Investment + Profit$$ Profit is calculated as a percentage of the Investment. Equating the incomes from both years will allow us to isolate the initial investment variable. ### Step-by-Step Solution * **Year 2010 Analysis:** Let the investment in 2010 be $I$. Profit percentage = $20\%$. Profit = $0.20 \times I$. Income in 2010 = $I + 0.20I = 1.20I$. * **Year 2011 Analysis:** Investment is less by ₹ 5000, so Investment in 2011 = $(I - 5000)$. Profit percentage increases by $6\%$, so new profit percentage = $20\% + 6\% = 26\%$. Income in 2011 = Investment + Profit Income in 2011 = $(I - 5000) + 0.26(I - 5000)$ Income in 2011 = $1.26(I - 5000)$. * **Equating the Incomes:** The problem states Income in 2011 = Income in 2010. $1.26(I - 5000) = 1.20I$ $1.26I - 1.26(5000) = 1.20I$ $1.26I - 6300 = 1.20I$ $1.26I - 1.20I = 6300$ $0.06I = 6300$ * **Solving for I:** $I = \frac{6300}{0.06} = \frac{630000}{6} = 105,000$. ### Exam Strategy & Shortcut Instead of expanding brackets immediately, leverage ratios. Income is a multiplier of investment: $1.2 \times I_{2010} = 1.26 \times I_{2011}$ $\frac{I_{2010}}{I_{2011}} = \frac{1.26}{1.20} = \frac{126}{120} = \frac{21}{20}$. The ratio of investments is 21:20. The difference in parts is $21 - 20 = 1$ part. We know the difference in actual investment is ₹ 5000. So, $1$ part = $5000$. Investment in 2010 is $21$ parts = $21 \times 5000 = 1,05,000$. This ratio method removes decimals and solves the problem in seconds! ### Common Pitfall Adding 6% to 20% to get 26% is correct, but students sometimes mistakenly calculate the new profit as $20\% \times 1.06$ instead of a direct absolute increase of percentage points. "Increased by 6%" means $20 + 6 = 26$. ### Final Answer **Therefore, the correct answer is ₹ 1,05,000.**