The shopkeeper sells his goods at 10% discount on the marked price. What price should he mark on an article that cost him 900 to gain 10% ?

Let’s solve this problem step by step:

1. **Cost Price (CP) of the article**: The shopkeeper's cost price is given as 900.

2. **Required Gain**: The shopkeeper wants a gain of 10% on his cost price. 
   
   To calculate the selling price (SP) that includes the desired gain:
   \[
   \text{SP} = \text{CP} \times \left(1 + \frac{\text{Gain \%}}{100}\right) = 900 \times \left(1 + \frac{10}{100}\right) = 900 \times 1.10 = 990
   \]

3. **Discount Offered**: The shopkeeper gives a 10% discount on the marked price (MP).

4. **Relation Between Selling Price and Marked Price**: The selling price is 90% of the marked price due to the 10% discount:
   \[
   \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount \%}}{100}\right) = \text{MP} \times 0.90
   \]

5. **Finding the Marked Price**: Substitute the selling price calculated earlier:
   \[
   990 = \text{MP} \times 0.90
   \]
   Solving for MP:
   \[
   \text{MP} = \frac{990}{0.90} = 1100
   \]

Therefore, the shopkeeper should mark the article at **1100** to achieve a 10% gain after giving a 10% discount.

Would you like more details on this solution? Here are some related questions:

1. How would the marked price change if the shopkeeper wanted a 20% gain?
2. What if the shopkeeper gave a 15% discount instead? How would it affect the marked price?
3. How can we calculate the discount percentage needed to achieve a specific gain?
4. How does increasing the cost price affect the selling strategy?
5. What is the impact of changing the gain percentage on the final selling price?

**Tip:** When calculating profit or loss, always distinguish between the cost price, selling price, and marked price to avoid confusion.

The shopkeeper sells his goods at 10% discount on the marked price. What price should he mark on an article that cost him 900 to gain 10%?

Discover how to determine the marked price of an article that costs 900 to achieve a 10% profit after giving a 10% discount. This step-by-step solution explores key concepts in percentage, profit and loss, and discounts, ideal for students in Grades 6-8.

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