A dealer purchased a washing machine for Rs.7660. 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 will follow these steps:

### Step 1: Understand the given information
- Cost Price (CP) of the washing machine = Rs. 7660
- Discount on the marked price = 12%
- Gain = 10%

### Step 2: Calculate the Selling Price (SP)
The Selling Price can be calculated using the formula:
\[ SP = CP + \text{Gain} \]
Since Gain is given as a percentage, we can express it as:
\[ \text{Gain} = \frac{\text{Gain Percent}}{100} \times CP \]
Substituting the values:
\[ \text{Gain} = \frac{10}{100} \times 7660 = 0.1 \times 7660 = 766 \]
Now, we can find the Selling Price:
\[ SP = CP + \text{Gain} = 7660 + 766 = 8426 \]

### Step 3: Relate Selling Price to Marked Price
The Selling Price is also related to the Marked Price (MP) and the discount given:
\[ SP = MP - \text{Discount} \]
The discount is 12% of the Marked Price:
\[ \text{Discount} = \frac{12}{100} \times MP = 0.12 \times MP \]
Thus, we can write:
\[ 8426 = MP - 0.12 \times MP \]
This simplifies to:
\[ 8426 = 0.88 \times MP \]

### Step 4: Solve for Marked Price (MP)
To find the Marked Price, we can rearrange the equation:
\[ MP = \frac{8426}{0.88} \]
Calculating this gives:
\[ MP = 9575 \]

### Conclusion
The marked price of the washing machine is Rs. 9575.

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