i bought a fridge three years back for rs 9000 the current price of a similar fridge is rs 16000.if i sell my fridge in the condition it is in.i would get rs 10500.instead if i get it painted for rs 3000 i can sell it for the price of a new one.what discount can i offer, if i expect to make the same percentage profit as i would have made.if i sell it without painting?

Let's break this down step by step:

### Step 1: Calculate the percentage profit if you sell the fridge without painting it.

- **Cost price of the fridge:** Rs 9,000
- **Selling price without painting:** Rs 10,500

The profit you make without painting is:

\[
\text{Profit without painting} = \text{Selling price} - \text{Cost price} = 10,500 - 9,000 = Rs 1,500
\]

The percentage profit is:

\[
\text{Percentage profit without painting} = \left( \frac{\text{Profit without painting}}{\text{Cost price}} \right) \times 100 = \left( \frac{1,500}{9,000} \right) \times 100 = 16.67\%
\]

### Step 2: Calculate the profit you would make after painting it.

- **Cost price of fridge (after painting):** Rs 9,000 (initial cost) + Rs 3,000 (painting cost) = Rs 12,000
- **Selling price after painting (same as new price):** Rs 16,000

The profit you would make after painting is:

\[
\text{Profit after painting} = \text{Selling price after painting} - \text{Total cost price} = 16,000 - 12,000 = Rs 4,000
\]

### Step 3: Determine the selling price with discount, such that the percentage profit remains the same.

You want to offer a discount on the painted fridge but still make the same percentage profit of 16.67%.

Let the new selling price be \( x \). We want the percentage profit to remain 16.67%, so the equation is:

\[
\frac{x - 12,000}{12,000} \times 100 = 16.67
\]

Simplifying:

\[
\frac{x - 12,000}{12,000} = 0.1667
\]

Multiplying both sides by 12,000:

\[
x - 12,000 = 2,000
\]

Adding 12,000 to both sides:

\[
x = 14,000
\]

### Step 4: Calculate the discount.

The original price of the new fridge is Rs 16,000, and you can sell it for Rs 14,000 while maintaining the same percentage profit. So, the discount is:

\[
\text{Discount} = 16,000 - 14,000 = Rs 2,000
\]

### Conclusion:
The discount you can offer, while still making the same percentage profit as you would have made without painting, is Rs 2,000.

---

Would you like further details on any part of this? 

Here are some related questions for practice:
1. What is the percentage increase from Rs 9,000 to Rs 16,000?
2. How much loss would you incur if you sell the fridge at Rs 8,500?
3. What would your percentage profit be if you sold the painted fridge for Rs 15,000?
4. What is the breakeven price if you had bought the fridge for Rs 10,000 instead?
5. How much extra profit would you make if you sold the painted fridge for Rs 17,000?

**Tip:** Always factor in additional costs like repairs or painting when calculating final profits.

Learn how to calculate profit and determine the discount using percentage concepts. Solve a practical problem involving the purchase and resale of a fridge, including the impact of additional costs like painting. Suitable for Grades 9-12.

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