A shopkeeper mark his goods at such a price that after allowinga discount of 12.5% on the mark price he can earn a profit of 20%. If the article cost him Rs 1400 then find its mark price.

Options

A. a)Rs 1920
B. b)Rs 1820
C. c)Rs 1780
D. d)Rs 1620

Answer

To find the mark price of the article, we can follow these steps:

### Step 1: Understand the given information
- Cost Price (CP) = Rs 1400
- Discount = 12.5%
- Profit = 20%

### Step 2: Calculate the Selling Price (SP)
The selling price can be calculated using the formula for profit:
\[ SP = CP + \text{Profit} \]
The profit is calculated as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times CP \]
Substituting the values:
\[ \text{Profit} = \frac{20}{100} \times 1400 = 280 \]
Now, substituting back to find SP:
\[ SP = 1400 + 280 = 1680 \]

### Step 3: Relate SP to Mark Price (MP)
The selling price after a discount is given by:
\[ SP = MP - \text{Discount} \]
The discount can be calculated as:
\[ \text{Discount} = \frac{12.5}{100} \times MP \]
Thus, we can write:
\[ SP = MP - \frac{12.5}{100} \times MP \]
This simplifies to:
\[ SP = MP \left(1 - \frac{12.5}{100}\right) = MP \left(\frac{87.5}{100}\right) \]

### Step 4: Set up the equation
Now we can set up the equation using the SP we calculated:
\[ 1680 = MP \left(\frac{87.5}{100}\right) \]

### Step 5: Solve for Mark Price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{1680 \times 100}{87.5} \]
Calculating this gives:
\[ MP = \frac{168000}{87.5} \]
To simplify:
\[ MP = \frac{1680000}{875} = 1920 \]

### Conclusion
The mark price of the article is Rs 1920.