Every month, Kritika spends 30% of her income on house rent and then spends 60% of the remaining amount on household expenditure.\nIf after these expenses she saves ₹ 6300 per month, what is her total monthly income?

Introduction / Context:
This question deals with successive percentage deductions from an income: first on rent and then on household expenses taken from the remaining balance. The amount left after these deductions represents savings. You are asked to work backwards from the savings to find Kritika's total monthly income. Problems like this test your ability to handle successive percentages and reverse calculations.

Given Data / Assumptions:

• Let Kritika's monthly income be I rupees.
• She spends 30% of I on house rent.
• She then spends 60% of the remaining amount on household expenditure.
• The amount left after these expenses is her monthly savings, equal to ₹ 6300.
• No other income sources or expenses are mentioned.

Concept / Approach:
We apply percentages step by step. First, 30% of I is spent on rent, leaving 70% of I. Then, 60% of this remaining 70% is spent on household expenses, leaving 40% of the remaining amount as savings. Therefore, savings equal a fixed fraction of the original income. Once we express savings as a percentage of I, we can set this equal to 6300 and solve for I by simple algebra.

Step-by-Step Solution:
Step 1: Let monthly income be I. Step 2: Rent = 30% of I = 0.30I. Remaining after rent = I − 0.30I = 0.70I. Step 3: Household expenditure = 60% of the remaining 0.70I = 0.60 * 0.70I = 0.42I. Step 4: Total expenses on rent and household = 0.30I + 0.42I = 0.72I. Step 5: Savings = income − total expenses = I − 0.72I = 0.28I. Step 6: Given savings are ₹ 6300, so 0.28I = 6300. Step 7: Solve for I: I = 6300 / 0.28. Step 8: Compute 6300 / 0.28 = 630000 / 28 = 22,500. Step 9: Therefore, Kritika's monthly income is ₹ 22,500.

Verification / Alternative check:
Check the calculations using I = ₹ 22,500. Rent = 30% of 22,500 = 0.30 * 22,500 = 6750. Remaining = 22,500 − 6750 = 15,750. Household expenses = 60% of 15,750 = 0.60 * 15,750 = 9450. Total expenses = 6750 + 9450 = 16,200. Savings = 22,500 − 16,200 = 6300, which matches the given savings. Thus, the calculated income is consistent.

Why Other Options Are Wrong:
₹ 22,000, ₹ 20,500, ₹ 25,000, and ₹ 18,000: Substituting any of these values into the same calculation results in savings different from ₹ 6300. For example, with ₹ 25,000 income, savings would be 28% of 25,000 = 7000, not 6300.

Common Pitfalls:
A frequent mistake is to subtract 30% and 60% directly from 100% to conclude that expenses are 90% and savings 10%. This ignores the fact that the 60% is applied to the remaining 70%, not to the original income. Another error is to treat 60% as being calculated on the full income instead of on the remainder. Always apply percentages in the correct order and base them on the amount specified in the problem.

Final Answer:
Kritika's total monthly income is ₹ 22,500.