Math Problem Statement

Ram loses 20% of his money. After spending 25% of the remainder, he has₹ 480 left. How much money did he originally have?

Solution

Let the original amount of money Ram had be xx.

Step 1: Loss of 20% of the money

When Ram loses 20%, he is left with 80% of his original money. So, after the loss, the remaining amount is: 0.80x0.80x

Step 2: Spending 25% of the remainder

Ram then spends 25% of the remaining money. The remaining money after spending 25% is 75% of what he had after the 20% loss: 0.75×0.80x=0.60x0.75 \times 0.80x = 0.60x

Step 3: Final Amount

We are told that after all this, Ram has ₹480 left. Therefore, we can set up the equation: 0.60x=4800.60x = 480

Step 4: Solving for xx

To find the original amount of money, divide both sides of the equation by 0.60: x=4800.60=800x = \frac{480}{0.60} = 800

So, Ram originally had ₹800.


Would you like a more detailed breakdown, or do you have any questions about this? Here are some related questions you might find useful:

  1. What happens if Ram spends 30% of the remaining money instead of 25%?
  2. How can we calculate the percentage of money lost if we only know the final amount?
  3. What are the effects of a 10% increase instead of a 20% decrease in the starting amount?
  4. How can this kind of problem be applied to real-life financial scenarios?
  5. How would the result change if the final amount was ₹600 instead of ₹480?

Tip: In problems like this, always break it into stages (percentage loss and then percentage expenditure) to make the math simpler.

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Math Problem Analysis

Mathematical Concepts

Percentage
Algebra
Equation Solving

Formulas

Remaining amount after percentage loss: (100% - loss%) × original amount
Remaining amount after percentage spending: (100% - spending%) × previous amount

Theorems

Basic percentage and proportion theorem

Suitable Grade Level

Grades 6-8