A man spends 15 percent of his income. If his expenditure is Rs 75, what is his total income in rupees?

Introduction / Context:
This simple percentage problem connects a known expenditure with an unknown total income through a given percentage. It is a direct application of reverse percentage and is very common in profit and loss and basic arithmetic sections.

Given Data / Assumptions:
Let total income be I. Man spends 15 percent of his income. Expenditure is given as Rs 75. We must find I.

Concept / Approach:
If a percentage of a quantity is known, we can write an equation relating them. Here 15 percent of income equals 75. So 15/100 * I = 75. Solving this equation for I gives the total income. This is a straightforward reverse percentage calculation.

Step-by-Step Solution:
We know 15 percent of I = 75. Write 15 percent as 15 / 100. Thus (15 / 100) * I = 75. This simplifies to 0.15I = 75. Divide both sides by 0.15. I = 75 / 0.15. Compute 75 / 0.15 = 75 * (1 / 0.15). Since 0.15 = 15 / 100, 1 / 0.15 = 100 / 15 = 20/3. Thus I = 75 * 20/3 = 75 * 20 / 3. Compute 75 / 3 = 25, so I = 25 * 20 = 500. Therefore the total income is Rs 500.

Verification / Alternative check:
Check by forward calculation. Fifteen percent of 500 is 15/100 * 500 = 75. This matches the stated expenditure. Hence the reverse percentage calculation is correct and consistent with the data.

Why Other Options Are Wrong:
If income were 400, 15 percent of 400 would be 60. For 300, expenditure would be 45. For 750, expenditure would be 112.5. For 600, expenditure would be 90. None of these equal 75. Only income of 500 gives 75 as 15 percent of income.

Common Pitfalls:
Sometimes students take 15 percent of 75 instead of viewing 75 as 15 percent of income. Others mistakenly subtract 15 from 75 rather than working with percentages. Translating the language into the correct equation before calculating prevents such errors.

Final Answer:
The man's total income is Rs 500.