Two shopkeepers sell a radio of similar brand and type at the same list price of Rs. 1000. The first allows two successive discounts of `20%` and `10%` and the second allows two successive discounts `15%` and `15%`. Find the difference in the discounts offered by the two shopkeepers.

Options

A. Rs. 3.50
B. Rs. 2.50
C. Rs. 1.50
D. Rs. 1.75

Answer

To find the difference in the discounts offered by the two shopkeepers, we will calculate the selling price after discounts for each shopkeeper and then determine the total discount given by each. Finally, we will find the difference between the two discounts.

### Step-by-Step Solution

1. **Determine the Selling Price for the First Shopkeeper:**
- The first shopkeeper offers two successive discounts of 20% and 10%.
- The list price of the radio is Rs. 1000.
- First, calculate the price after the first discount (20%):
\[ \text{Price after 20% discount} = 1000 - (20\% \text{ of } 1000) = 1000 - 200 = 800 \]
- Now, apply the second discount (10%) on the new price (Rs. 800):
\[ \text{Price after 10% discount} = 800 - (10\% \text{ of } 800) = 800 - 80 = 720 \]
- Thus, the selling price for the first shopkeeper is Rs. 720.

2. **Determine the Selling Price for the Second Shopkeeper:**
- The second shopkeeper offers two successive discounts of 15% and 15%.
- Again, the list price of the radio is Rs. 1000.
- First, calculate the price after the first discount (15%):
\[ \text{Price after 15% discount} = 1000 - (15\% \text{ of } 1000) = 1000 - 150 = 850 \]
- Now, apply the second discount (15%) on the new price (Rs. 850):
\[ \text{Price after 15% discount} = 850 - (15\% \text{ of } 850) = 850 - 127.5 = 722.5 \]
- Thus, the selling price for the second shopkeeper is Rs. 722.5.

3. **Calculate the Discounts Offered by Each Shopkeeper:**
- The discount offered by the first shopkeeper:
\[ \text{Discount} = \text{List Price} - \text{Selling Price} = 1000 - 720 = 280 \]
- The discount offered by the second shopkeeper:
\[ \text{Discount} = \text{List Price} - \text{Selling Price} = 1000 - 722.5 = 277.5 \]

4. **Find the Difference in Discounts:**
- Now, calculate the difference between the discounts offered by the two shopkeepers:
\[ \text{Difference} = 280 - 277.5 = 2.5 \]

### Final Answer:
The difference in the discounts offered by the two shopkeepers is Rs. 2.5.