A man saves 20% of his monthly salary. Due to an increase in the cost of living, he has to increase his monthly expenses by 15%, and now he is able to save only Rs. 400 per month. What is his monthly salary?

Introduction / Context:
This question combines percentage savings and percentage increase in expenses to determine the original salary. Initially the man saves a fixed proportion of his salary, and then due to a 15% rise in expenses his monthly saving drops to a fixed rupee amount. Such problems appear frequently in aptitude tests to check understanding of how savings, expenses and income relate to each other when percentages change.

Given Data / Assumptions:

• Initially, the man saves 20% of his salary.
• Therefore, he spends 80% of his salary originally.
• His expenses then increase by 15%.
• After the increase, his remaining saving becomes Rs. 400 per month.
• His monthly salary remains the same before and after the increase.
• We must find the amount of his monthly salary.

Concept / Approach:
Let the salary be S. Initially, expenses = 0.80S and savings = 0.20S. When expenses increase by 15%, the new expenses become 1.15 times the old expenses, that is 1.15 * 0.80S. The new saving is then S minus these increased expenses. This new saving is given as Rs. 400. By equating S - 1.15 * 0.80S to 400, we get a simple linear equation in S which can be solved to obtain the salary.

Step-by-Step Solution:
Step 1: Let monthly salary = S rupees. Step 2: Initial saving = 20% of S = 0.20S. Step 3: Initial expenses = 80% of S = 0.80S. Step 4: Expenses increase by 15%, so new expenses = 0.80S * 1.15. Step 5: Compute new expenses factor: 0.80 * 1.15 = 0.92, so new expenses = 0.92S. Step 6: New saving = S - new expenses = S - 0.92S = 0.08S. Step 7: This new saving is given as Rs. 400, so 0.08S = 400. Step 8: Solve for S: S = 400 / 0.08 = 400 * (100 / 8) = 400 * 12.5 = Rs. 5,000.

Verification / Alternative check:
If S = Rs. 5,000, then initially he saves 20% of 5,000 = Rs. 1,000 and spends Rs. 4,000. After the rise, his new expenses are 4,000 * 1.15 = Rs. 4,600. His new saving is 5,000 - 4,600 = Rs. 400, which matches the information given in the question, confirming that the monthly salary is Rs. 5,000.

Why Other Options Are Wrong:
If the salary were Rs. 4,500, Rs. 6,000, Rs. 6,500, or Rs. 4,000, the new savings computed via the same percentage increases would not equal Rs. 400. For example, with S = 6,000, new expenses would be 0.92 * 6,000 = 5,520 and the new saving would be 6,000 - 5,520 = 480, which does not match the given saving.

Common Pitfalls:
A frequent error is to increase the salary instead of the expenses, or to misapply the 15% increase directly to the salary instead of to the original expenses. Another common mistake is to add 15 percentage points to the 80% expenses incorrectly, rather than multiplying by 1.15. Keeping track that expenses are a fraction of salary and that the increase applies to that fraction avoids these mistakes.

Final Answer:
The man's monthly salary is Rs. 5,000.