A dealer purchased a washing ma chine for 7,660. After allowing a discount of 12% on its marked price, he still gains 10%. Find the marked price of the washing machine.

Options

A. 9575
B. 8426
C. 8246
D. 79755

Answer

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

### Step 1: Understand the given values
- Cost Price (CP) = ₹7,660
- Discount = 12%
- Profit = 10%

### Step 2: Use the formula for the relationship between CP, MP, Discount, and Profit
The formula to relate the Cost Price (CP), Marked Price (MP), Discount, and Profit is:
\[ \frac{CP}{MP} = \frac{100 - D}{100 + P} \]
Where:
- D = Discount percentage
- P = Profit percentage

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ \frac{7660}{MP} = \frac{100 - 12}{100 + 10} \]
This simplifies to:
\[ \frac{7660}{MP} = \frac{88}{110} \]

### Step 4: Simplify the fraction
Now we simplify the fraction on the right:
\[ \frac{88}{110} = \frac{8}{10} = \frac{4}{5} \]
Thus, we have:
\[ \frac{7660}{MP} = \frac{4}{5} \]

### Step 5: Cross multiply to find MP
Cross multiplying gives us:
\[ 4 \times MP = 5 \times 7660 \]
Calculating the right side:
\[ 5 \times 7660 = 38300 \]
So we have:
\[ 4 \times MP = 38300 \]

### Step 6: Solve for MP
Now, divide both sides by 4:
\[ MP = \frac{38300}{4} = 9575 \]

### Conclusion
The marked price of the washing machine is ₹9,575.