A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains `Rs. 56 on one item, his advertised price of the item, in Rs. , is

Options

A. 820
B. 780
C. 790
D. 800

Answer

To solve the problem step by step, we will break down the information given and apply the relevant formulas.

### Step 1: Understand the given information
- The shopkeeper allows a commission of 23% on the advertised price (MP).
- He makes a profit of 10% on the cost price (CP).
- The profit in rupees is Rs. 56.

### Step 2: Set up the equations
Let’s denote:
- Cost Price (CP) = Rs. 100 (for simplicity, we can use any value since we will find the ratio)
- Selling Price (SP) = CP + Profit = 100 + 10% of CP = 100 + 10 = Rs. 110.

### Step 3: Relate the profit to the given value
Since the profit is given as Rs. 56, we can set up the equation:
- Profit = SP - CP
- Rs. 56 = SP - CP
- SP = CP + 56 = 100 + 56 = Rs. 156.

### Step 4: Find the Selling Price in terms of CP
From the profit percentage:
- SP = CP + (10/100) * CP = 110% of CP = 1.1 * CP.

### Step 5: Calculate the Selling Price
Since we assumed CP = Rs. 100, we can calculate:
- SP = 1.1 * 100 = Rs. 110.

### Step 6: Relate Selling Price to the Mark Price (MP)
The relationship between Selling Price (SP), Mark Price (MP), and discount is given by:
- SP = MP * (1 - Discount Percentage).
- Here, Discount Percentage = 23% = 0.23.
- Therefore, SP = MP * (1 - 0.23) = MP * 0.77.

### Step 7: Substitute the Selling Price into the equation
We have SP = Rs. 110:
- 110 = MP * 0.77.

### Step 8: Solve for the Mark Price (MP)
To find MP, rearrange the equation:
- MP = 110 / 0.77.

Calculating this gives:
- MP = 110 / 0.77 ≈ Rs. 142.86.

### Step 9: Find the Advertised Price
Now, we need to relate this back to the commission:
- If the shopkeeper allows a 23% commission on the advertised price, we need to find the advertised price (AP).
- We know that after allowing a 23% discount, the selling price is Rs. 110.

Let’s denote the Advertised Price as AP:
- SP = AP * (1 - 0.23) = AP * 0.77.
- Therefore, 110 = AP * 0.77.

### Step 10: Solve for Advertised Price (AP)
Rearranging gives:
- AP = 110 / 0.77.

Calculating this gives:
- AP = 110 / 0.77 ≈ Rs. 142.86.

### Conclusion
The advertised price of the item is approximately Rs. 142.86.