A trader sold an article at profit 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 find the cost price of the article, let's break down the problem step by step:

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( 100x \).

### Step 2: Calculate the Selling Price with 20% Profit
The selling price (SP) when sold at a profit of 20% can be calculated using the formula:
\[ SP = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
Substituting the values:
\[ SP = 100x \times \left(1 + \frac{20}{100}\right) = 100x \times \frac{120}{100} = 120x \]

### Step 3: Calculate the New Cost Price with 60% Less Price
If the trader had bought the article at 60% less price, the new cost price (CP') would be:
\[ CP' = CP \times \left(1 - \frac{60}{100}\right) = 100x \times \frac{40}{100} = 40x \]

### Step 4: Calculate the Selling Price with 50% Profit on New Cost Price
If he sold it at a profit of 50%, the new selling price (SP') would be:
\[ SP' = CP' \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
Substituting the values:
\[ SP' = 40x \times \left(1 + \frac{50}{100}\right) = 40x \times \frac{150}{100} = 60x \]

### Step 5: Set Up the Equation Based on the Problem Statement
According to the problem, if he sold it for Rs. 90 less than the original selling price, we can set up the equation:
\[ SP' = SP - 90 \]
Substituting the values we found:
\[ 60x = 120x - 90 \]

### Step 6: Solve for x
Rearranging the equation:
\[ 90 = 120x - 60x \]
\[ 90 = 60x \]
\[ x = \frac{90}{60} = 1.5 \]

### Step 7: Calculate the Cost Price
Now, substituting the value of \( x \) back into the cost price formula:
\[ CP = 100x = 100 \times 1.5 = 150 \]

### Final Answer
The value of the cost price is \( \text{Rs. } 150 \).

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