An article was sold at 35% gain. Had it been sold for Rs 600 more, then the gain would have been 40%. What is the cost price (in Rs) of the article?

Options

A. 12000
B. 13200
C. 12500
D. 14000

Answer

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

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

### Step 2: Calculate Selling Price at 35% Gain
The selling price (SP) when sold at a 35% gain can be expressed as:
\[ SP = CP + 0.35 \times CP = 1.35 \times CP \]

### Step 3: Calculate Selling Price at 40% Gain
If the article were sold for Rs 600 more, the selling price would be:
\[ SP_{new} = SP + 600 = 1.35 \times CP + 600 \]
At this selling price, the gain would be 40%, so we can express it as:
\[ SP_{new} = CP + 0.40 \times CP = 1.40 \times CP \]

### Step 4: Set Up the Equation
Now, we can set the two expressions for \( SP_{new} \) equal to each other:
\[ 1.35 \times CP + 600 = 1.40 \times CP \]

### Step 5: Solve for CP
Rearranging the equation gives:
\[ 600 = 1.40 \times CP - 1.35 \times CP \]
\[ 600 = 0.05 \times CP \]
Now, divide both sides by 0.05 to find \( CP \):
\[ CP = \frac{600}{0.05} = 12000 \]

### Step 6: Conclusion
The cost price of the article is Rs 12,000.

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