A trader sold an article at proft of 20%. Had he bought that article at 60% less price and sold it at Rs. 90 less, he would have gained 50%. What is the value (In Rs.) of cost price?

Options

A. 150
B. 200
C. 250
D. 300

Answer

To solve the problem step by step, let's define the variables and break down the information given in the question.

### Step 1: Define the Variables
Let the original cost price (CP) of the article be \( x \).

### Step 2: Calculate the Selling Price (SP) with 20% Profit
The trader sells the article at a profit of 20%. Therefore, the selling price (SP) can be calculated as:
\[ SP = CP + 20\% \text{ of } CP = x + 0.2x = 1.2x \]

### Step 3: Calculate the New Cost Price (CP) if Bought at 60% Less
If the trader had bought the article at 60% less, the new cost price would be:
\[ \text{New CP} = x - 60\% \text{ of } x = x - 0.6x = 0.4x \]

### Step 4: Calculate the New Selling Price (SP) for 50% Profit
If he sold it at Rs. 90 less than the original SP, the new selling price would be:
\[ \text{New SP} = SP - 90 = 1.2x - 90 \]
Given that this new SP gives him a profit of 50%, we can express this as:
\[ \text{New SP} = \text{New CP} + 50\% \text{ of New CP = } 0.4x + 0.5 \times 0.4x = 0.4x + 0.2x = 0.6x \]

### Step 5: Set Up the Equation
Now we can set up the equation based on the new selling price:
\[ 1.2x - 90 = 0.6x \]

### Step 6: Solve for x
Rearranging the equation:
\[ 1.2x - 0.6x = 90 \]
\[ 0.6x = 90 \]
\[ x = \frac{90}{0.6} = 150 \]

### Step 7: Conclusion
The original cost price (CP) of the article is:
\[ \text{Cost Price} = 150 \text{ Rs.} \]