Ritu sold an article at a loss of 12%. Had she sold it for ₹55.80 more, she would have gained 13%. To gain 10%, she must sell it for ₹:

Options

A. 274.8
B. 280.46
C. 245.52
D. 271.6

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article based on the information given about the selling prices at different profit and loss percentages.

### Step 1: Understand the given information
- Ritu sold the article at a loss of 12%.
- If she had sold it for ₹55.80 more, she would have gained 13%.

### Step 2: Let the cost price (CP) of the article be ₹x.
- Selling Price (SP) at a loss of 12% can be calculated as:
\[ SP_{loss} = CP - (12\% \text{ of } CP) = x - 0.12x = 0.88x \]

- Selling Price (SP) at a gain of 13% can be calculated as:
\[ SP_{gain} = CP + (13\% \text{ of } CP) = x + 0.13x = 1.13x \]

### Step 3: Set up the equation based on the information given
According to the problem, if Ritu sold the article for ₹55.80 more than the selling price at a loss, she would gain 13%. Thus, we can write:
\[ 0.88x + 55.80 = 1.13x \]

### Step 4: Solve the equation
Rearranging the equation gives:
\[ 55.80 = 1.13x - 0.88x \]
\[ 55.80 = 0.25x \]

Now, solving for x:
\[ x = \frac{55.80}{0.25} = 223.20 \]

So, the cost price (CP) of the article is ₹223.20.

### Step 5: Calculate the selling price for a gain of 10%
To find the selling price for a gain of 10%, we calculate:
\[ SP_{gain\ 10\%} = CP + (10\% \text{ of } CP) = x + 0.10x = 1.10x \]
Substituting the value of x:
\[ SP_{gain\ 10\%} = 1.10 \times 223.20 = 245.52 \]

### Final Answer
To gain 10%, Ritu must sell the article for ₹245.52.

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