A trader purchased a washing machine for Rs. 10,000. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.

Answer

To find the marked price of the washing machine, we can follow these steps:

### Step 1: Determine the Selling Price (SP)
The trader purchased the washing machine for Rs. 10,000 and gains a profit of 10%. The Selling Price (SP) can be calculated using the formula:

\[ SP = CP + (Profit \% \times CP) \]

Where:
- CP = Cost Price = Rs. 10,000
- Profit % = 10%

Calculating the SP:

\[ SP = 10,000 + \left( \frac{10}{100} \times 10,000 \right) = 10,000 + 1,000 = 11,000 \]

### Step 2: Set Up the Equation for Marked Price (MP)
Let the Marked Price (MP) be denoted as \( X \). The trader allows a discount of 12% on the marked price. The Selling Price can also be expressed in terms of the Marked Price:

\[ SP = MP - (Discount \% \times MP) \]

Substituting the values we have:

\[ 11,000 = X - \left( \frac{12}{100} \times X \right) \]

### Step 3: Simplify the Equation
We can simplify the equation:

\[ 11,000 = X - 0.12X \]
\[ 11,000 = 0.88X \]

### Step 4: Solve for Marked Price (MP)
To find \( X \), we rearrange the equation:

\[ X = \frac{11,000}{0.88} \]

Calculating \( X \):

\[ X = 12,500 \]

### Conclusion
The marked price of the washing machine is Rs. 12,500.

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