A dealer makes a profit of 20% even after giving a 10% discount on the advertised price of a scooter. If he makes a profit of 7500 on the sale of the scooter.the advertised price was

Options

A. 45000
B. 47500
C. 50000
D. 52500

Answer

To find the advertised price (MP) of the scooter, we can follow these steps:

### Step 1: Understand the Profit and Discount
- The dealer makes a profit of 20% on the cost price (CP).
- The dealer gives a discount of 10% on the advertised price (MP).
- The profit earned on the sale of the scooter is ₹7500.

### Step 2: Set Up the Relationships
- Let the Cost Price (CP) be represented as \( CP \).
- The Selling Price (SP) can be calculated using the profit percentage:
\[ SP = CP + 20\% \text{ of } CP = CP + 0.2 \times CP = 1.2 \times CP \]

### Step 3: Calculate Selling Price from Profit
- We know that the profit earned is ₹7500. Therefore:
\[ SP - CP = 7500 \]
Substituting the expression for SP:
\[ 1.2 \times CP - CP = 7500 \]
Simplifying this gives:
\[ 0.2 \times CP = 7500 \]
\[ CP = \frac{7500}{0.2} = 37500 \]

### Step 4: Calculate Selling Price (SP)
- Now, we can calculate the Selling Price (SP):
\[ SP = 1.2 \times CP = 1.2 \times 37500 = 45000 \]

### Step 5: Relate Selling Price to Advertised Price (MP)
- The dealer gives a discount of 10% on the advertised price (MP):
\[ SP = MP - 10\% \text{ of } MP = MP - 0.1 \times MP = 0.9 \times MP \]
Therefore, we can set up the equation:
\[ 45000 = 0.9 \times MP \]

### Step 6: Solve for Advertised Price (MP)
- To find MP, we rearrange the equation:
\[ MP = \frac{45000}{0.9} = 50000 \]

### Conclusion
- The advertised price (MP) of the scooter is **₹50000**.

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