An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 12 .5 % on it. The cost price of the article is :

Options

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

Answer

To find the cost price (CP) of the article, we can follow these steps:

### Step 1: Define the Cost Price
Let the cost price of the article be \( X \).

### Step 2: Calculate Selling Price at 10% Loss
If 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: Calculate Selling Price at 12.5% Gain
If the article is sold for Rs. 9 more, it results in a gain of 12.5%. The selling price in this case can be calculated as:
\[ SP = CP + (12.5\% \text{ of } CP) = X + 0.125X = 1.125X \]

### Step 4: Set Up the Equation
According to the problem, selling the article for Rs. 9 more results in the selling price being:
\[ 0.9X + 9 = 1.125X \]

### Step 5: Rearrange the Equation
Now, we can rearrange the equation to isolate \( X \):
\[ 1.125X - 0.9X = 9 \]
\[ 0.225X = 9 \]

### Step 6: Solve for Cost Price
To find \( X \), divide both sides by 0.225:
\[ X = \frac{9}{0.225} \]
\[ X = 40 \]

### Conclusion
The cost price of the article is \( \text{Rs. } 40 \).

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