Step 1: Understanding the Question:
The question asks for the final sale price of an appliance after two successive discounts are applied to its marked price of Rs. 4580.
The discounts of 20% and 35% are applied consecutively, meaning the second discount is calculated on the price remaining after the first discount has been deducted.
Step 2: Key Formula or Approach:
We can solve this using either the step-by-step reduction method or by finding the single equivalent discount using the percentage formula:
\[ \text{Effective Discount %} = d_1 + d_2 - \frac{d_1 \times d_2}{100} \]
Using sequential multiplication:
\[ \text{Final Sale Price} = \text{Original Price} \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \]
Step 3: Detailed Explanation:
1. Let us find the single equivalent discount percentage first.
2. Given successive discounts are \( d_1 = 20% \) and \( d_2 = 35% \).
3. Applying the formula for the single equivalent discount:
\[ \text{Equivalent Discount %} = 20 + 35 - \frac{20 \times 35}{100} \]
\[ \text{Equivalent Discount %} = 55 - \frac{700}{100} = 55 - 7 = 48% \]
4. Therefore, the total discount on the marked price is 48%.
5. The final sale price is the remaining percentage of the original price, which is:
\[ 100% - 48% = 52% \]
6. Now, we calculate 52% of the original cost price of Rs. 4580:
\[ \text{Final Sale Price} = \frac{52}{100} \times 4580 \]
\[ \text{Final Sale Price} = 0.52 \times 4580 = 2381.60 \text{ Rs.} \]
7. Rounding Rs. 2381.60 to the nearest rupee gives Rs. 2382.
8. Alternatively, applying the discounts one after the other:
Price after the first 20% discount:
\[ 4580 - (0.20 \times 4580) = 4580 - 916 = 3664 \text{ Rs.} \]
Price after the second 35% discount applied to Rs. 3664:
\[ 3664 - (0.35 \times 3664) = 3664 - 1282.4 = 2381.6 \text{ Rs.} \]
Rounding Rs. 2381.6 to the nearest integer gives Rs. 2382.
Step 4: Final Answer:
The final sale price of the food processor is Rs. 2382.