Rahul bought a sweater and saved Rs. 20 when a discount of 25% was given. What was the price of the sweater before the discount?

Question

Accepted Answer

To determine the original price of the sweater before the discount, we need to understand the relationship between the discount percentage, the amount saved, and the original price.

1. **Understanding the Discount**: 
   - Rahul saved Rs. 20 due to a 25% discount. This means that Rs. 20 represents 25% of the original price of the sweater.

2. **Calculating the Original Price**:
   - Let the original price of the sweater be $ P $.
   - According to the problem, 25% of $ P $ is equal to Rs. 20.
   - Mathematically, this can be expressed as:
     $$
     0.25 \times P = 20
     $$
   - To find $ P $, divide both sides of the equation by 0.25:
     $$
     P = \frac{20}{0.25} = 80
     $$
   - Therefore, the original price of the sweater is Rs. 80.

3. **Justification for Option 1**:
   - Option 1 states that the original price is Rs. 80, which matches our calculated original price. Hence, Option 1 is correct.

4. **Explanation for Incorrectness of Other Options**:
   - **Option 2 (Rs. 90)**: If the original price were Rs. 90, then 25% of Rs. 90 would be Rs. 22.50, not Rs. 20. Therefore, this option is incorrect.
   - **Option 3 (Rs. 75)**: If the original price were Rs. 75, then 25% of Rs. 75 would be Rs. 18.75, not Rs. 20. Therefore, this option is incorrect.
   - **Option 4 (Rs. 95)**: If the original price were Rs. 95, then 25% of Rs. 95 would be Rs. 23.75, not Rs. 20. Therefore, this option is incorrect.

In conclusion, based on the calculations and logical reasoning, Option 1 is the correct answer, as it accurately reflects the original price of the sweater before the discount was applied.