A shopkeeper incurs `10%` loss by selling a washing machine for Rs 16200. At what price should the washing machine be sold to earn `15%` profit?

Options

A. Rs 18700
B. Rs. 19700
C. Rs 20700
D. Rs 20250

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Determine the Cost Price (CP)
We know that the shopkeeper incurs a 10% loss when selling the washing machine for Rs. 16,200. The formula for loss percentage is:

\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{Cost Price}} \times 100 \]

Given that the loss percentage is 10%, we can express the loss as:

\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]

Substituting the values we have:

\[ 10 = \frac{\text{CP} - 16200}{\text{CP}} \times 100 \]

### Step 2: Rearranging the Equation
We can rearrange the equation to isolate CP:

\[ \frac{\text{CP} - 16200}{\text{CP}} = \frac{10}{100} \]

This simplifies to:

\[ \frac{\text{CP} - 16200}{\text{CP}} = \frac{1}{10} \]

### Step 3: Cross-Multiplying
Cross-multiplying gives us:

\[ 10(\text{CP} - 16200) = \text{CP} \]

### Step 4: Simplifying the Equation
Expanding the left side:

\[ 10\text{CP} - 162000 = \text{CP} \]

Now, we can move all terms involving CP to one side:

\[ 10\text{CP} - \text{CP} = 162000 \]

This simplifies to:

\[ 9\text{CP} = 162000 \]

### Step 5: Solving for CP
Now, divide both sides by 9:

\[ \text{CP} = \frac{162000}{9} = 18000 \]

### Step 6: Calculate the Selling Price for 15% Profit
Now that we have the Cost Price (CP), we need to find the Selling Price (SP) for a 15% profit. The formula for Selling Price is:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Where profit can be calculated as:

\[ \text{Profit} = \frac{15}{100} \times \text{CP} \]

Substituting the value of CP:

\[ \text{Profit} = \frac{15}{100} \times 18000 = 2700 \]

### Step 7: Final Selling Price Calculation
Now, we can calculate the Selling Price:

\[ \text{SP} = \text{CP} + \text{Profit} = 18000 + 2700 = 20700 \]

Thus, the washing machine should be sold for **Rs. 20,700** to earn a 15% profit.

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