If an article is sold for Rs 550 then the profit is 10%. At what price should the article be sold to make 10% loss?

Options

A. Rs 450
B. Rs 460
C. Rs 300
D. Rs 470

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article based on the given selling price (SP) and profit percentage. Then, we will calculate the selling price for a 10% loss.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) is Rs 550 and the profit is 10%, we can use the formula for selling price:

\[ SP = CP + \text{Profit} \]

Since profit is 10% of the cost price (CP), we can express this as:

\[ \text{Profit} = \frac{10}{100} \times CP = 0.1 \times CP \]

Substituting this into the SP formula gives:

\[ SP = CP + 0.1 \times CP = 1.1 \times CP \]

Now, we can set up the equation:

\[ 550 = 1.1 \times CP \]

To find CP, we rearrange the equation:

\[ CP = \frac{550}{1.1} \]

Calculating this gives:

\[ CP = 500 \]

### Step 2: Calculate Selling Price for 10% Loss
Now that we have the cost price (CP) as Rs 500, we need to find the selling price (SP) that would result in a 10% loss.

The formula for selling price at a loss is:

\[ SP = CP - \text{Loss} \]

The loss is 10% of the cost price:

\[ \text{Loss} = \frac{10}{100} \times CP = 0.1 \times 500 = 50 \]

Now substituting this back into the SP formula gives:

\[ SP = 500 - 50 = 450 \]

### Conclusion
Thus, the selling price at which the article should be sold to incur a 10% loss is Rs 450.

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