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?

Options

A. Rs. 54400
B. Rs. 52400
C. Rs. 48600
D. Rs. 58640

Answer

To solve the problem step by step, we will follow the information given in the question and derive the necessary values.

### Step 1: Let the Market Price (MP) be Rs. 100
We assume the market price of the article is Rs. 100 for simplicity in calculations.

### Step 2: Calculate Selling Price (SP) at 37% Discount
When the article is sold at a 37% discount:
- Discount = 37% of MP = 37% of 100 = Rs. 37
- Selling Price (SP) = MP - Discount = 100 - 37 = Rs. 63

### Step 3: Calculate Cost Price (CP) with 9% Loss
Since the shopkeeper suffers a 9% loss when selling at Rs. 63:
- Loss = 9% of CP
- Selling Price (SP) = CP - Loss
- Therefore, 63 = CP - (9% of CP)
- This means 63 = CP - 0.09 * CP
- 63 = 0.91 * CP
- CP = 63 / 0.91 = Rs. 69.23 (approximately)

### Step 4: Calculate Selling Price (SP) at 28% Discount
When the article is sold at a 28% discount:
- Discount = 28% of MP = 28% of 100 = Rs. 28
- Selling Price (SP) = MP - Discount = 100 - 28 = Rs. 72

### Step 5: Calculate the Difference in Selling Prices
The difference in selling prices between the two discounts:
- Difference = SP at 28% discount - SP at 37% discount
- Difference = 72 - 63 = Rs. 9

### Step 6: Relate the Difference to the Cost Price
According to the problem, this difference of Rs. 9 corresponds to the Rs. 7072 more the shopkeeper earns when selling at a 28% discount:
- 9 = 7072 / (SP at 28% discount - SP at 37% discount)
- This means that Rs. 7072 corresponds to the additional amount earned when selling at the higher discount.

### Step 7: Calculate the Selling Price for No Profit No Loss
To find the selling price that results in no profit and no loss, we need to sell at the Cost Price (CP):
- Selling Price for No Profit No Loss = CP = Rs. 69.23 (approximately)

### Final Answer
The price at which the shopkeeper should sell to get no profit and no loss is approximately **Rs. 69.23**.

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