Sequential spending and balance: From salary S, 10% is house rent; of the remainder, 15% is spent on children’s education; of the new balance, 10% is spent on clothes. If ₹1377 remains, what is S?

Introduction / Context:
This is a chain-percentage problem on successive remainders. Each percentage is taken on the current balance, not on the original salary. Convert each step to a multiplier and multiply to get the final fraction of S that remains.

Given Data / Assumptions:

• S = salary.
• Rent = 10% ⇒ balance = 0.90S.
• Education = 15% of balance ⇒ new balance = 0.85 * 0.90S.
• Clothes = 10% of balance ⇒ final balance = 0.90 * 0.85 * 0.90S.
• Final balance = ₹1377.

Concept / Approach:
Compute the net multiplier: 0.90 * 0.85 * 0.90 = 0.6885. Then 0.6885S = 1377 ⇒ solve S = 1377 / 0.6885. Use fraction reduction to avoid rounding errors.

Step-by-Step Solution:
Net factor = 0.90 * 0.85 * 0.90 = 0.68850.6885S = 1377 ⇒ S = 1377 / 0.6885Using 0.6885 = 6885/10000, S = 1377 * 10000 / 6885 = 2000

Verification / Alternative check:
Forward: 2000 → 1800 → (−15%) 1530 → (−10%) 1377. Matches the given final amount.

Why Other Options Are Wrong:
2040, 2100, 2200 do not reproduce ₹1377 after the specified deductions.

Common Pitfalls:
Adding percentages directly (10% + 15% + 10%) rather than compounding them on the successive balances.

Final Answer:
Rs. 2000