An article is sold at a loss of 10%. Had it been sold for 9 more, there would have been a gain of 12 `1/2`% on it. The cost price of the article is:

Options

A. A) 40
B. B) 45
C. C) 50
D. D) 35

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the Cost Price
Let's assume the cost price (CP) of the article is \( 100x \).

**Hint:** Start by defining a variable for the cost price to make calculations easier.

### Step 2: Calculate the Selling Price at a Loss
Since the article is sold at a loss of 10%, the selling price (SP1) can be calculated as:
\[ SP1 = CP - 10\% \text{ of } CP = 100x - 10\% \text{ of } 100x = 100x - 10x = 90x \]

**Hint:** Remember that selling at a loss means the selling price is less than the cost price.

### Step 3: Calculate the Selling Price for Profit
If the article were sold for Rs 9 more, there would be a gain of \( 12.5\% \). The selling price (SP2) in this case would be:
\[ SP2 = CP + 12.5\% \text{ of } CP = 100x + 12.5\% \text{ of } 100x = 100x + 12.5x = 112.5x \]

**Hint:** When calculating profit, add the percentage of the cost price to the cost price itself.

### Step 4: Set Up the Equation
According to the problem, the difference between the two selling prices is Rs 9:
\[ SP2 - SP1 = 9 \]
Substituting the values we calculated:
\[ 112.5x - 90x = 9 \]

**Hint:** This equation represents the relationship between the two selling prices and the additional amount.

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ 22.5x = 9 \]

**Hint:** Combine like terms to isolate the variable.

### Step 6: Solve for x
To find the value of \( x \), divide both sides by 22.5:
\[ x = \frac{9}{22.5} \]

**Hint:** When dividing, ensure you simplify the fraction to find the value of \( x \).

### Step 7: Calculate the Cost Price
Now we need to find the cost price:
\[ CP = 100x = 100 \times \frac{9}{22.5} \]
To simplify:
\[ CP = \frac{900}{22.5} = 40 \]

**Hint:** Multiply the simplified value of \( x \) by 100 to find the cost price.

### Final Answer
The cost price of the article is Rs 40.

**Hint:** Always check your answer against the options provided to ensure it matches.