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

Options

A. ₹ 200
B. ₹ 850
C. ₹ 750
D. ₹ 900

Answer

To solve the problem step-by-step, we will follow the given information and perform the necessary calculations.

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

### Step 2: Calculate the Cost Price (CP)
To find the Cost Price (CP), we can use the formula for profit:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Given that the profit is 15% of the Cost Price, we can express this as:
\[ \text{Profit} = 0.15 \times \text{CP} \]
Thus, we can rewrite the Selling Price formula as:
\[ SP = CP + 0.15 \times CP = 1.15 \times CP \]
Now, substituting the Selling Price:
\[ 5865 = 1.15 \times CP \]

### Step 3: Solve for Cost Price (CP)
To find CP, we rearrange the equation:
\[ CP = \frac{5865}{1.15} \]
Calculating this gives:
\[ CP = 5100 \]

### Step 4: Understand the Discount
The retailer bought the cellphone at a discount of 15%. This means the Cost Price (CP) is 85% of the marked price (MP). We can express this as:
\[ CP = 0.85 \times MP \]
We already calculated CP as ₹5100, so we can set up the equation:
\[ 5100 = 0.85 \times MP \]

### Step 5: Solve for Marked Price (MP)
To find the Marked Price, we rearrange the equation:
\[ MP = \frac{5100}{0.85} \]
Calculating this gives:
\[ MP = 6000 \]

### Step 6: Calculate the Discount Amount
The discount amount can be calculated as:
\[ \text{Discount} = MP - CP \]
Substituting the values we found:
\[ \text{Discount} = 6000 - 5100 = 900 \]

### Conclusion
The discount on the cellphone is ₹900.