Successive changes on money in hand: A person loses 20% of his money. He then spends 25% of the remainder and is left with ₹480. What amount did he originally have?

Introduction / Context:This problem uses successive percentage changes on an unknown amount. The final remainder is given, and we work backward to the original sum.

Given Data / Assumptions:

• Original amount = X.
• After losing 20%, remainder = 80% of X = 0.8X.
• He then spends 25% of this remainder, so he keeps 75% of it.
• Final amount left = ₹480.

Concept / Approach:Apply successive multipliers: Final = X * 0.8 * 0.75. Solve for X using the given final amount.

Step-by-Step Solution:

Verification / Alternative check:Check forward: Start 800 ⇒ after −20% ⇒ 640 ⇒ spend 25% of 640 (which is 160) ⇒ left 480. Works perfectly.

Why Other Options Are Wrong:

• ₹600, ₹720, ₹840, ₹1000 do not produce ₹480 after the given successive changes.

Common Pitfalls:Adding or subtracting percentages arithmetically instead of using multiplicative factors for successive changes.

Final Answer:₹800