The marked price of an article is 8440 rupees. It is sold for 7440 rupees. If there is a loss of 7%, then by what percent above the cost is the article marked?

Options

A. 5
B. 8
C. `6 (1)/(2)`
D. `5 (1)/(2)`

Answer

To solve the problem step by step, we will first determine the cost price of the article and then calculate the percentage by which the marked price exceeds the cost price.

### Step 1: Determine the Selling Price and Loss Percentage
The selling price (SP) of the article is given as Rs. 7440, and the loss percentage is given as 7%.

### Step 2: Calculate the Cost Price
To find the cost price (CP) when there is a loss, we can use the formula:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Rearranging the formula to find CP:
\[ \text{CP} = \frac{\text{SP}}{1 - \frac{\text{Loss \%}}{100}} \]
Substituting the values:
\[ \text{CP} = \frac{7440}{1 - \frac{7}{100}} = \frac{7440}{0.93} \]
Calculating:
\[ \text{CP} = \frac{7440}{0.93} \approx 8000 \]

### Step 3: Determine the Marked Price
The marked price (MP) of the article is given as Rs. 8440.

### Step 4: Calculate the Difference Between Marked Price and Cost Price
Now, we find the difference between the marked price and the cost price:
\[ \text{Difference} = \text{MP} - \text{CP} = 8440 - 8000 = 440 \]

### Step 5: Calculate the Percentage Above Cost Price
To find the percentage by which the marked price is above the cost price, we use the formula:
\[ \text{Percentage} = \left(\frac{\text{Difference}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage} = \left(\frac{440}{8000}\right) \times 100 \]
Calculating:
\[ \text{Percentage} = 5.5\% \]

### Final Answer
The article is marked at **5.5%** above the cost price.

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