An article is sold at a loss of 10%. Had it been sold for 90 more, there would have been a gain of 59. The original sale price of the article (in) :

Options

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

Answer

To solve the problem step by step, we will denote the cost price (CP) of the article as \( CP \).

### Step 1: Understand the Loss Percentage
The article is sold at a loss of 10%. This means that the selling price (SP) is 90% of the cost price.

\[ SP = CP \times \frac{90}{100} = 0.9 \times CP \]

**Hint:** Remember that a loss of 10% means you are selling the article for 90% of its cost price.

### Step 2: Set Up the Equation for Selling Price with Gain
If the article were sold for 90 rupees more, there would be a gain of 59 rupees. This means the new selling price (SP') would be:

\[ SP' = SP + 90 \]

Since this new selling price gives a profit of 59 rupees, we can express it as:

\[ SP' = CP + 59 \]

**Hint:** When calculating profit, the selling price is equal to the cost price plus the profit amount.

### Step 3: Substitute the Selling Price
Now, we can substitute \( SP \) from Step 1 into the equation for \( SP' \):

\[ SP + 90 = CP + 59 \]

Substituting \( SP = 0.9 \times CP \):

\[ 0.9 \times CP + 90 = CP + 59 \]

**Hint:** This is a crucial step where you combine the information about the selling price and the profit.

### Step 4: Rearranging the Equation
Now, let's rearrange the equation to isolate \( CP \):

\[ 0.9 \times CP + 90 - CP = 59 \]

This simplifies to:

\[ -0.1 \times CP + 90 = 59 \]

Now, subtract 90 from both sides:

\[ -0.1 \times CP = 59 - 90 \]

\[ -0.1 \times CP = -31 \]

**Hint:** When isolating variables, make sure to perform the same operation on both sides of the equation.

### Step 5: Solve for Cost Price
Now, divide both sides by -0.1 to find \( CP \):

\[ CP = \frac{-31}{-0.1} = 310 \]

**Hint:** Dividing by a negative number will change the sign, so be careful with your signs.

### Step 6: Calculate the Original Selling Price
Now that we have the cost price, we can find the original selling price:

\[ SP = 0.9 \times CP = 0.9 \times 310 = 279 \]

**Hint:** To find the selling price at a loss, multiply the cost price by the percentage that represents the selling price.

### Final Answer
The original selling price of the article is:

\[ \boxed{279} \]