If cost price is Rs 50 less than the selling price and profit is 10%, then what is the selling price (in Rs)?

Options

A. A)450
B. B)500
C. C)550
D. D)600

Answer

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

### Step 1: Define the Variables
Let the Selling Price (SP) be represented as \( SP \) and the Cost Price (CP) be represented as \( CP \).

### Step 2: Set Up the Relationship
According to the problem, the Cost Price is Rs. 50 less than the Selling Price. We can express this relationship mathematically:
\[ CP = SP - 50 \]

### Step 3: Understand the Profit Percentage
The problem states that the profit is 10%. Profit can be calculated using the formula:
\[ \text{Profit} = SP - CP \]
Since the profit is 10% of the Cost Price, we can express this as:
\[ \text{Profit} = 0.10 \times CP \]

### Step 4: Substitute CP in the Profit Formula
We can substitute the expression for \( CP \) from Step 2 into the profit formula:
\[ SP - (SP - 50) = 0.10 \times (SP - 50) \]

### Step 5: Simplify the Equation
Now, simplify the left side:
\[ SP - SP + 50 = 0.10 \times (SP - 50) \]
This simplifies to:
\[ 50 = 0.10 \times (SP - 50) \]

### Step 6: Expand and Solve for SP
Now, expand the right side:
\[ 50 = 0.10 \times SP - 5 \]
Add 5 to both sides to isolate the term with SP:
\[ 50 + 5 = 0.10 \times SP \]
\[ 55 = 0.10 \times SP \]

### Step 7: Solve for SP
To find \( SP \), divide both sides by 0.10:
\[ SP = \frac{55}{0.10} \]
\[ SP = 550 \]

### Conclusion
Thus, the Selling Price (SP) is Rs. 550.