A retailer purchases a grinder at a discount of 15% and sells it for Rs. 1955 at a profit of 15%. The amount of discount received by retailer from the wholesaler was

Options

A. Rs. 270
B. Rs. 290
C. Rs. 300
D. Rs. 330

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Problem
The retailer purchases a grinder at a discount of 15% and sells it for Rs. 1955 at a profit of 15%. We need to find the amount of discount received by the retailer from the wholesaler.

### Step 2: Define Variables
Let:
- \( MP \) = Marked Price (the original price before discount)
- \( CP \) = Cost Price (the price the retailer pays after discount)
- \( SP \) = Selling Price = Rs. 1955
- Discount = 15% of \( MP \)

### Step 3: Calculate the Selling Price in Terms of Cost Price
Since the retailer sells the grinder at a profit of 15%, we can express the Selling Price in terms of Cost Price:
\[ SP = CP + (15\% \text{ of } CP) = 1.15 \times CP \]
Given that \( SP = 1955 \), we can write:
\[ 1955 = 1.15 \times CP \]

### Step 4: Calculate the Cost Price
To find \( CP \), we rearrange the equation:
\[ CP = \frac{1955}{1.15} \]
Calculating this gives:
\[ CP = 1700 \]

### Step 5: Relate Cost Price to Marked Price
The retailer purchases the grinder at a discount of 15%. Therefore, the Cost Price can also be expressed as:
\[ CP = MP - (15\% \text{ of } MP) = MP - 0.15 \times MP = 0.85 \times MP \]
Substituting the value of \( CP \):
\[ 1700 = 0.85 \times MP \]

### Step 6: Calculate the Marked Price
Now, we can find \( MP \):
\[ MP = \frac{1700}{0.85} \]
Calculating this gives:
\[ MP = 2000 \]

### Step 7: Calculate the Discount Amount
The discount received by the retailer is 15% of the Marked Price:
\[ \text{Discount} = 15\% \text{ of } MP = 0.15 \times 2000 \]
Calculating this gives:
\[ \text{Discount} = 300 \]

### Final Answer
The amount of discount received by the retailer from the wholesaler is Rs. 300.

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