Radhika bought a car for ₹ 2,50,000. Next year its price decreased by 10% and in next year it further decreased by 12%. In the two years overall decrease percent in the price of car is

Question

Accepted Answer

Here's a detailed explanation justifying why Option 3 is correct and why the other options are incorrect:

**Justification for Option 3 (20.80%) being correct:**

To find the overall decrease percentage, we need to calculate the car's price after each successive decrease and then determine the total percentage drop from the original price.

1.  **Initial Price of the car:** ₹ 2,50,000

2.  **Price after the first year's decrease (10%):**
    *   Decrease amount = 10% of ₹ 2,50,000 = (10/100) * 2,50,000 = ₹ 25,000
    *   Price after 1st year = ₹ 2,50,000 - ₹ 25,000 = ₹ 2,25,000

3.  **Price after the second year's decrease (12%):**
    *   This decrease is applied to the price after the first year, which is ₹ 2,25,000.
    *   Decrease amount = 12% of ₹ 2,25,000 = (12/100) * 2,25,000 = ₹ 27,000
    *   Price after 2nd year = ₹ 2,25,000 - ₹ 27,000 = ₹ 1,98,000

4.  **Total decrease in price over two years:**
    *   Total decrease = Original Price - Price after 2nd year
    *   Total decrease = ₹ 2,50,000 - ₹ 1,98,000 = ₹ 52,000

5.  **Overall decrease percentage:**
    *   Overall decrease percentage = (Total decrease / Original Price) * 100
    *   Overall decrease percentage = (₹ 52,000 / ₹ 2,50,000) * 100
    *   Overall decrease percentage = (52 / 250) * 100
    *   Overall decrease percentage = 0.208 * 100 = 20.8%

Alternatively, using successive percentage change multipliers:
*   After a 10% decrease, the price is 100% - 10% = 90% of the original price (multiplier = 0.90).
*   After a 12% further decrease, the price is 100% - 12% = 88% of the price after the first decrease (multiplier = 0.88).
*   Final price as a percentage of original price = (0.90 * 0.88) * 100% = 0.792 * 100% = 79.2%
*   Overall decrease percentage = 100% - 79.2% = 20.8%

Both methods confirm that the overall decrease percent is 20.80%.

**Why other options are incorrect:**

*   **Option 1: 3.20%**
    This value is significantly lower than the actual decrease and does not result from any standard calculation of successive percentage decreases. It might arise from an incorrect subtraction or miscalculation, such as (12-10)/100 * 100 = 2%, which is still not 3.2%.

*   **Option 2: 22%**
    This option is obtained by simply adding the two percentage decreases (10% + 12% = 22%). This is incorrect because the second decrease (12%) is applied to the *reduced* price after the first year, not to the original price. When successive percentage changes occur, they are applied to the new base amount, not the initial base amount for each change.

*   **Option 4: 8%**
    This value is also too low and does not correspond to the correct calculation for successive percentage decreases. It might be a result of an incorrect subtraction or misinterpretation of the problem.

Therefore, based on the calculations, Option 3, 20.80%, is the correct answer.