An article is sold at a loss of 10%. Had it been sold for Rs.90 more, there would have been a gain of 5%. The original sale price of the article (inRs. ) is

Options

A. 650
B. 540
C. 600
D. 628

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the cost price (CP) of the article be Rs. \( x \).

### Step 2: Determine the Selling Price at a Loss of 10%
When the article is sold at a loss of 10%, the selling price (SP) can be calculated as:
\[ SP = CP - (10\% \text{ of } CP) = x - 0.1x = 0.9x \]

### Step 3: Determine the Selling Price for a Gain of 5%
If the article had been sold for Rs. 90 more, there would have been a gain of 5%. Therefore, the new selling price would be:
\[ SP_{new} = SP + 90 = 0.9x + 90 \]
And this selling price can also be expressed in terms of the cost price:
\[ SP_{new} = CP + (5\% \text{ of } CP) = x + 0.05x = 1.05x \]

### Step 4: Set Up the Equation
Now we can set the two expressions for the new selling price equal to each other:
\[ 0.9x + 90 = 1.05x \]

### Step 5: Solve the Equation
Rearranging the equation gives:
\[ 90 = 1.05x - 0.9x \]
\[ 90 = 0.15x \]
Now, divide both sides by 0.15 to find \( x \):
\[ x = \frac{90}{0.15} = 600 \]

### Step 6: Calculate the Original Selling Price
Now that we have the cost price, we can find the original selling price when sold at a loss of 10%:
\[ SP = 0.9x = 0.9 \times 600 = 540 \]

### Final Answer
The original sale price of the article is Rs. **540**.

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