A man sold an article for Rs 560 and gained 12%, the cost price of the article was-

Options

A. Rs 450
B. Rs 550
C. Rs 400
D. Rs 500

Answer

To find the cost price of the article sold for Rs 560 with a gain of 12%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Profit Percentage
The selling price (SP) is given by the formula:
\[ SP = CP + \text{Profit} \]
Where profit can also be expressed in terms of percentage:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times CP \]

### Step 2: Set up the equation
Given that the selling price (SP) is Rs 560 and the profit percentage is 12%, we can write:
\[ 560 = CP + \frac{12}{100} \times CP \]

### Step 3: Combine like terms
We can combine the terms on the right side:
\[ 560 = CP \left(1 + \frac{12}{100}\right) \]
This simplifies to:
\[ 560 = CP \left(\frac{100 + 12}{100}\right) \]
\[ 560 = CP \left(\frac{112}{100}\right) \]

### Step 4: Solve for Cost Price (CP)
To isolate CP, we can rearrange the equation:
\[ CP = 560 \times \frac{100}{112} \]

### Step 5: Calculate CP
Now, we can calculate the value:
\[ CP = \frac{560 \times 100}{112} \]
\[ CP = \frac{56000}{112} \]
\[ CP = 500 \]

### Conclusion
The cost price of the article was Rs 500.

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