Deepak sold study table for Rupees 2231 at a loss of 3% at what price should he sell it so as to gain 5% solve correctly with using the correct formula

To solve this problem, we'll follow these steps:

### 1. Determine the cost price (C.P.) of the study table
Given:
- Selling Price (S.P.) = ₹2231
- Loss = 3%

We know the formula for loss percentage:
\[
\text{Loss %} = \frac{\text{C.P.} - \text{S.P.}}{\text{C.P.}} \times 100
\]

Rearranging to solve for the cost price (C.P.):
\[
\text{C.P.} = \frac{\text{S.P.} \times 100}{100 - \text{Loss %}}
\]

Substituting the given values:
\[
\text{C.P.} = \frac{2231 \times 100}{100 - 3} = \frac{2231 \times 100}{97} = \frac{223100}{97} = ₹2300
\]

So, the cost price of the study table is ₹2300.

### 2. Determine the selling price to gain 5%
To find the new selling price (S.P.) for a 5% gain, we use the formula:
\[
\text{S.P.} = \text{C.P.} \times \left(1 + \frac{\text{Gain %}}{100}\right)
\]

Substituting the cost price and the desired gain percentage:
\[
\text{S.P.} = 2300 \times \left(1 + \frac{5}{100}\right) = 2300 \times 1.05 = ₹2415
\]

So, Deepak should sell the study table at **₹2415** to gain 5%.

Would you like any further details or have any questions?

Here are 5 related questions you might want to explore:
1. How would the selling price change if the desired gain was 10% instead of 5%?
2. What is the formula for calculating the cost price if the gain percentage and selling price are given?
3. How does the loss percentage affect the cost price in similar problems?
4. What if Deepak wanted a 7% loss—how would we calculate the selling price?
5. How would the formulas change if Deepak gave a discount after determining the selling price?

**Tip**: Always check your percentage-based calculations carefully to avoid small errors, especially when dealing with decimals!

Deepak sold a study table for ₹2231 at a loss of 3%. At what price should he sell it so as to gain 5%?

Learn how to calculate the selling price to gain 5% after selling at a loss of 3%. This problem explores profit and loss concepts and key formulas for percentage calculations. Suitable for students in Grades 6-8.

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