An article was sold at 10% gain. Had It been sold for Rs. 225 more, the gain would have been 25%. What is the cost price (in Rs.) of the article?

Options

A. 1000
B. 1200
C. 1500
D. 2000

Answer

To solve the problem step by step, let's denote the cost price (CP) of the article as \( CP \).

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

### Step 2: Calculate Selling Price at 10% Gain
If the article is sold at a 10% gain, the selling price (SP1) can be calculated as:
\[ SP1 = CP + 10\% \text{ of } CP = x + 0.1x = 1.1x \]

### Step 3: Calculate Selling Price at 25% Gain
If the article is sold for Rs. 225 more, the selling price (SP2) would be:
\[ SP2 = SP1 + 225 = 1.1x + 225 \]
At a 25% gain, the selling price can also be expressed as:
\[ SP2 = CP + 25\% \text{ of } CP = x + 0.25x = 1.25x \]

### Step 4: Set Up the Equation
Since both expressions represent the same selling price (SP2), we can set them equal to each other:
\[ 1.1x + 225 = 1.25x \]

### Step 5: Solve for x
Now, we will solve for \( x \):
\[ 225 = 1.25x - 1.1x \]
\[ 225 = 0.15x \]
\[ x = \frac{225}{0.15} \]
\[ x = 1500 \]

### Step 6: Conclusion
The cost price of the article is \( \text{Rs. } 1500 \).

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