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 (inRs) is

Options

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

Answer

To solve the problem step-by-step, we will follow the reasoning and calculations outlined in the video transcript.

### Step 1: Understand the Given Information
- The shopkeeper allows a **23% commission** (which is equivalent to a discount) on the advertised price.
- He makes a **10% profit** on the cost price.
- The profit amount is **Rs 56**.

### Step 2: Establish the Relationship Between Selling Price and Advertised Price
Let the **advertised price (AP)** be denoted as **MP** (Marked Price).

The selling price (SP) after allowing a 23% discount can be calculated as:
\[ SP = MP \times (1 - 0.23) = MP \times 0.77 \]
This is our **Equation 1**.

### Step 3: Establish the Relationship Between Selling Price and Cost Price
Since the shopkeeper makes a **10% profit**, we can express the selling price in terms of the cost price (CP):
\[ SP = CP \times (1 + 0.10) = CP \times 1.10 \]
This is our **Equation 2**.

### Step 4: Find the Cost Price Using the Profit Amount
We know that the profit amount is Rs 56. Since profit is defined as:
\[ \text{Profit} = SP - CP \]
And given that the profit percentage is 10%, we can express it as:
\[ 0.10 \times CP = 56 \]
From this, we can find the cost price:
\[ CP = \frac{56}{0.10} = 560 \]

### Step 5: Substitute the Cost Price into Equation 2
Now, we substitute \( CP = 560 \) into Equation 2:
\[ SP = 1.10 \times 560 = 616 \]

### Step 6: Substitute the Selling Price into Equation 1
Now we substitute \( SP = 616 \) into Equation 1:
\[ 616 = 0.77 \times MP \]
To find the advertised price (MP), we rearrange this equation:
\[ MP = \frac{616}{0.77} \]

### Step 7: Calculate the Advertised Price
Now, we perform the calculation:
\[ MP = \frac{616}{0.77} \approx 800 \]

### Conclusion
The advertised price of the item is **Rs 800**.