The difference between cost price and selling price is Rs 451. If loss percentage is 11%, then what is the selling price (in Rs)?

Options

A. 3254
B. 3649
C. 3857
D. 4100

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between Cost Price (CP), Selling Price (SP), and Loss
The loss is defined as the difference between the cost price and the selling price. In this case, the loss is given as Rs 451. Therefore, we can express this relationship as:
\[ \text{CP} - \text{SP} = 451 \]

### Step 2: Define the loss percentage
The loss percentage is given as 11%. This means that the selling price is 11% less than the cost price. We can express this as:
\[ \text{SP} = \text{CP} - 0.11 \times \text{CP} = 0.89 \times \text{CP} \]

### Step 3: Substitute SP in the loss equation
Now, we can substitute the expression for SP into the loss equation:
\[ \text{CP} - (0.89 \times \text{CP}) = 451 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ \text{CP} - 0.89 \text{CP} = 451 \]
\[ 0.11 \text{CP} = 451 \]

### Step 5: Solve for CP
To find the cost price (CP), divide both sides by 0.11:
\[ \text{CP} = \frac{451}{0.11} \]
\[ \text{CP} = 4100 \]

### Step 6: Calculate the Selling Price (SP)
Now that we have the cost price, we can find the selling price using the formula:
\[ \text{SP} = 0.89 \times \text{CP} \]
\[ \text{SP} = 0.89 \times 4100 \]
\[ \text{SP} = 3649 \]

### Final Answer
Thus, the selling price (SP) is Rs 3649.

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