The marked price of an article is 300. The shopkeeper gives a discount of 10% on the marked price and still gains 25%. Then the cost price of the article is

Options

A. ₹ 216
B. ₹ 203.50
C. ₹ 237.50
D. ₹215

Answer

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

### Step 1: Calculate the Selling Price after Discount
The marked price (MP) of the article is given as Rs. 300. The shopkeeper gives a discount of 10% on this marked price.

**Calculation:**
- Discount = 10% of MP = 10/100 * 300 = Rs. 30
- Selling Price (SP) = MP - Discount = 300 - 30 = Rs. 270

### Step 2: Use the Profit Percentage to Find the Cost Price
The shopkeeper gains a profit of 25%. We can use the formula for profit percentage to find the cost price (CP).

**Profit Percentage Formula:**
\[ \text{Profit Percentage} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]

Given that the profit percentage is 25%, we can rewrite the formula:
\[ 25 = \frac{270 - \text{CP}}{\text{CP}} \times 100 \]

### Step 3: Rearranging the Equation
To solve for CP, we first rearrange the equation:
\[ \frac{270 - \text{CP}}{\text{CP}} = \frac{25}{100} \]
\[ \frac{270 - \text{CP}}{\text{CP}} = \frac{1}{4} \]

### Step 4: Cross-Multiply to Solve for CP
Cross-multiplying gives us:
\[ 4(270 - \text{CP}) = \text{CP} \]
\[ 1080 - 4\text{CP} = \text{CP} \]

### Step 5: Combine Like Terms
Now, we can combine like terms:
\[ 1080 = 5\text{CP} \]

### Step 6: Solve for CP
Now, divide both sides by 5 to find the cost price:
\[ \text{CP} = \frac{1080}{5} = 216 \]

Thus, the cost price of the article is Rs. 216.

### Summary of the Solution
- Marked Price = Rs. 300
- Discount = 10% of Rs. 300 = Rs. 30
- Selling Price = Rs. 300 - Rs. 30 = Rs. 270
- Profit = 25% implies SP = CP + 0.25 * CP
- Solving the equation gives CP = Rs. 216.