If cost price is Rs. 150 less than the selling price and profit is 20%, then what is the selling price (in Rs.)?

Options

A. 750
B. 800
C. 850
D. 900

Answer

To find the selling price (SP) given that the cost price (CP) is Rs. 150 less than the selling price and the profit is 20%, we can follow these steps:

### Step 1: Define the relationship between CP and SP
We know that:
\[ CP = SP - 150 \]

### Step 2: Understand the profit percentage
The profit is given as 20%. This means:
\[ Profit = SP - CP \]
Since profit is also defined as a percentage of the cost price, we can express it as:
\[ Profit = 20\% \times CP \]
or
\[ Profit = \frac{20}{100} \times CP = \frac{1}{5} \times CP \]

### Step 3: Set up the equation
From the profit definition, we can substitute CP:
\[ SP - CP = \frac{1}{5} \times CP \]
Now substituting \( CP \) from Step 1:
\[ SP - (SP - 150) = \frac{1}{5} \times (SP - 150) \]

### Step 4: Simplify the equation
This simplifies to:
\[ 150 = \frac{1}{5} \times (SP - 150) \]

### Step 5: Multiply both sides by 5 to eliminate the fraction
\[ 150 \times 5 = SP - 150 \]
\[ 750 = SP - 150 \]

### Step 6: Solve for SP
Now, add 150 to both sides:
\[ SP = 750 + 150 \]
\[ SP = 900 \]

### Conclusion
The selling price (SP) is Rs. 900.

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