Listen carefully okay TV set is Mark for rupees 12000 with discounted price of 11490 if payment is made cash find the rate of cash discount offered by the shopkeeper solve this in a very good way correctly

To find the rate of cash discount offered by the shopkeeper, we can follow these steps:

### Step 1: Identify the given information.
- Marked Price (MP) of the TV set = ₹12,000
- Discounted Price (SP) when paid in cash = ₹11,490

### Step 2: Calculate the actual discount.
The **actual discount** is the difference between the Marked Price (MP) and the Selling Price (SP):
\[
\text{Discount} = \text{MP} - \text{SP}
\]
\[
\text{Discount} = 12,000 - 11,490 = ₹510
\]

### Step 3: Calculate the discount rate.
The **discount rate** is the percentage of the Marked Price that was deducted as a discount. The formula for the discount rate is:
\[
\text{Discount Rate} = \left(\frac{\text{Discount}}{\text{MP}}\right) \times 100
\]
Substitute the values:
\[
\text{Discount Rate} = \left(\frac{510}{12,000}\right) \times 100
\]
\[
\text{Discount Rate} = \left(0.0425\right) \times 100 = 4.25\%
\]

### Final Answer:
The cash discount offered by the shopkeeper is **4.25%**.

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Would you like more details or further clarification?

Here are 5 related questions to deepen your understanding:
1. How do you calculate the percentage discount if you are given only the discount rate?
2. What would be the new price if the cash discount was 5% instead?
3. How do you calculate a markup percentage if given the cost price and selling price?
4. What is the difference between percentage markup and percentage discount?
5. How would the calculation change if taxes were included in the final price?

### Tip: 
Always double-check if the discount is based on the marked price or another price (like the selling price), as this changes the discount rate calculation.

Learn how to calculate the cash discount offered by the shopkeeper on a TV set marked at ₹12,000 with a discounted price of ₹11,490. The solution includes key formulas for calculating discount and discount rate, making it ideal for students in Grades 6-8.

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