When an article is sold at 37% discount a shopkeeper suffers 9% loss. But when it is sold at 28% discount, he gets Rs.7072 more than what he got on previous deal. At what price should he sell to get no profit no loss?

Let's denote the marked price of the article as \( M \) and the cost price of the article as \( C \).

### Step 1: Information from the 37% discount scenario
When the article is sold at a 37% discount, the shopkeeper suffers a 9% loss. This means the selling price in this case is 9% less than the cost price, or 91% of the cost price.

- Selling price with 37% discount = \( M \times (1 - 0.37) = 0.63M \).
- This selling price is also 91% of the cost price: \( 0.63M = 0.91C \).

Thus, from this, we can express the cost price in terms of the marked price:
\[
C = \frac{0.63M}{0.91}
\]
\[
C = \frac{63M}{91} = \frac{7M}{10}
\]
So, the cost price \( C = 0.7M \).

### Step 2: Information from the 28% discount scenario
When the article is sold at a 28% discount, the selling price is higher by Rs.7072 compared to the previous deal. 

- Selling price with 28% discount = \( M \times (1 - 0.28) = 0.72M \).
- The difference in selling price between the two scenarios is Rs.7072:
\[
0.72M - 0.63M = 7072
\]
\[
0.09M = 7072
\]
\[
M = \frac{7072}{0.09} = 78577.78
\]

Thus, the marked price \( M = Rs. 78,577.78 \).

### Step 3: Price for no profit no loss
For no profit and no loss, the selling price should be equal to the cost price, which we know is 70% of the marked price:
\[
C = 0.7 \times 78577.78 = Rs. 55,004.44
\]

Thus, the price at which the shopkeeper should sell the article to get no profit and no loss is **Rs. 55,004.44**.

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Do you want further details or have any questions?

Here are some related questions:
1. What is the relation between marked price, cost price, and selling price?
2. How do percentage discounts affect the selling price?
3. How can one calculate profit or loss percentage from selling price?
4. What happens if the shopkeeper wants a 10% profit?
5. What would the price be if the shopkeeper aimed for a 15% loss?

**Tip:** Always remember to express all terms (like cost price, selling price, and discounts) in relation to the marked price to simplify calculations.

Find the selling price for an article that gives no profit or loss after being sold at different discounts. The problem involves calculating percentage-based discounts and determining profit or loss based on selling and cost prices. Suitable for Grades 9-12 students.

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