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?
Aptitude
Percentage
Difficulty: Easy
Choose an option
-
A₹600
-
B₹720
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C₹800
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D₹840
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E₹1000
Answer
Correct Answer: ₹800
Explanation
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:
Final amount = X * 0.8 * 0.75 = X * 0.60.0.60X = 480.X = 480 / 0.60 = 800.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