Pavan sold an item at a loss of 12.5%. If he could have sold it for Rs. 56 more, he would have made a profit of 22.5%. What should be the selling price of the item to make a profit of 25% ?

Options

A. Rs. 200
B. Rs. 185
C. Rs. 182
D. Rs. 190

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the item and then calculate the selling price (SP) for a profit of 25%.

### Step 1: Understanding the Loss and Profit Situation
Pavan sold an item at a loss of 12.5%. This means:
- Selling Price (SP) at a loss = CP - (12.5% of CP)
- SP = CP - (0.125 * CP) = 0.875 * CP

If he sold it for Rs. 56 more, he would have made a profit of 22.5%. This means:
- New Selling Price (SP) = CP + (22.5% of CP)
- SP = CP + (0.225 * CP) = 1.225 * CP

### Step 2: Setting Up the Equation
According to the problem, the difference between the new selling price and the original selling price is Rs. 56:
\[ 1.225 \cdot CP - 0.875 \cdot CP = 56 \]

### Step 3: Simplifying the Equation
Now, simplify the left side:
\[ (1.225 - 0.875) \cdot CP = 56 \]
\[ 0.35 \cdot CP = 56 \]

### Step 4: Finding the Cost Price (CP)
Now, solve for CP:
\[ CP = \frac{56}{0.35} \]
\[ CP = 160 \]

### Step 5: Calculating Selling Price for 25% Profit
To find the selling price for a 25% profit:
- Selling Price (SP) = CP + (25% of CP)
- SP = CP + (0.25 * CP) = 1.25 * CP

Now substitute the value of CP:
\[ SP = 1.25 \cdot 160 \]
\[ SP = 200 \]

### Final Answer
The selling price of the item to make a profit of 25% is Rs. 200.

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