On selling an article for Rs 270, there is a gain of 12.5%. What is its cost price?

Options

A. Rs 240
B. Rs 220
C. Rs 210
D. Rs 250

Answer

To find the cost price (CP) of an article sold for Rs 270 with a gain of 12.5%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Gain Percentage
The gain percentage is given by the formula:
\[ \text{Gain Percentage} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]

### Step 2: Substitute the known values into the formula
We know:
- Selling Price (SP) = Rs 270
- Gain Percentage = 12.5%

Substituting these values into the formula:
\[ 12.5 = \frac{270 - \text{CP}}{\text{CP}} \times 100 \]

### Step 3: Simplify the equation
To simplify, we can first divide both sides by 100:
\[ 0.125 = \frac{270 - \text{CP}}{\text{CP}} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 0.125 \times \text{CP} = 270 - \text{CP} \]

### Step 5: Rearranging the equation
Rearranging the equation to isolate CP:
\[ 0.125 \times \text{CP} + \text{CP} = 270 \]
\[ (0.125 + 1) \times \text{CP} = 270 \]
\[ 1.125 \times \text{CP} = 270 \]

### Step 6: Solve for CP
Now, divide both sides by 1.125 to find CP:
\[ \text{CP} = \frac{270}{1.125} \]

### Step 7: Calculate the value
Calculating the value:
\[ \text{CP} = 240 \]

Thus, the cost price of the article is Rs 240.

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