A retailer buys a cellphone at a discount of 15% and sells it for Rs. 5865. Thus, he makes a profit of 15%. The discount is:

Options

A. Rs. 200
B. Rs. 850
C. Rs. 750
D. Rs. 900

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the Selling Price and Profit
The retailer sells the cellphone for Rs. 5865 and makes a profit of 15%.

### Step 2: Calculate the Cost Price (CP)
Let the Cost Price (CP) be \( x \).
Since the retailer makes a profit of 15%, we can express the Selling Price (SP) in terms of CP:
\[ SP = CP + 15\% \text{ of } CP = CP + 0.15 \times CP = 1.15 \times CP \]
Given that the Selling Price (SP) is Rs. 5865, we can set up the equation:
\[ 1.15 \times CP = 5865 \]

### Step 3: Solve for the Cost Price (CP)
Now, we can solve for CP:
\[ CP = \frac{5865}{1.15} \]
Calculating this gives:
\[ CP = 5100 \]

### Step 4: Calculate the Marked Price (MP)
The retailer buys the cellphone at a discount of 15%. Let the Marked Price (MP) be \( y \).
The relationship between the Marked Price and Cost Price is:
\[ CP = MP - \text{Discount} \]
Since the discount is 15% of the Marked Price:
\[ CP = MP - 0.15 \times MP = 0.85 \times MP \]
Thus, we can express the Marked Price in terms of Cost Price:
\[ MP = \frac{CP}{0.85} \]
Substituting the value of CP:
\[ MP = \frac{5100}{0.85} \]
Calculating this gives:
\[ MP = 6000 \]

### Step 5: Calculate the Discount
Now, we can find the discount amount:
\[ \text{Discount} = MP - CP = 6000 - 5100 = 900 \]

### Final Answer
Thus, the discount is Rs. 900.

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