Pankaj sells a trouser at a loss of 10%. If he buys it for 20% less price and sells it for Rs. 9 more, then he gains 15%. What is the cost price (in Rs) of the trouser?

Options

A. 450
B. 400
C. 350
D. 440

Answer

To solve the problem step by step, let's denote the cost price (CP) of the trouser as \( CP = 100x \).

### Step 1: Calculate Selling Price (SP) at 10% Loss
Pankaj sells the trouser at a loss of 10%. Therefore, the selling price (SP) when sold at a 10% loss is calculated as follows:
\[ SP = CP - (10\% \text{ of } CP) = 100x - 10x = 90x \]

### Step 2: Calculate New Cost Price (CP) after 20% Reduction
If Pankaj buys the trouser for 20% less than the original cost price, the new cost price becomes:
\[ \text{New CP} = CP - (20\% \text{ of } CP) = 100x - 20x = 80x \]

### Step 3: Calculate Selling Price (SP) after Selling for Rs. 9 More
According to the problem, if he sells it for Rs. 9 more than the previous SP, the new selling price is:
\[ \text{New SP} = SP + 9 = 90x + 9 \]

### Step 4: Calculate Profit Percentage
In this case, he gains 15% on the new cost price (80x). The formula for profit is:
\[ \text{Profit} = \text{New SP} - \text{New CP} \]
Given that the profit is 15% of the new cost price:
\[ \text{Profit} = 15\% \text{ of } 80x = 0.15 \times 80x = 12x \]
Thus, we can set up the equation:
\[ 90x + 9 - 80x = 12x \]

### Step 5: Solve the Equation
Now, simplify the equation:
\[ 90x + 9 - 80x = 12x \]
\[ 10x + 9 = 12x \]
Subtract \(10x\) from both sides:
\[ 9 = 12x - 10x \]
\[ 9 = 2x \]
Now, divide both sides by 2:
\[ x = \frac{9}{2} = 4.5 \]

### Step 6: Calculate the Original Cost Price (CP)
Now, substituting back to find the original cost price:
\[ CP = 100x = 100 \times 4.5 = 450 \]

### Final Answer
The cost price of the trouser is Rs. 450.

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