A shopkeeper marks an article at a price such that after giving a discount of 30%, the gains x%. If the cost price and the marked price of the article are Rs. 460 and Rs. 736 respectively, what is the value of x?

Options

A. `10%`
B. `15%`
C. `12%`
D. `16%`

Answer

To solve the problem step by step, we will calculate the selling price after the discount, find the profit, and then determine the gain percentage (x%).

### Step 1: Find the Selling Price after Discount
The marked price (MP) of the article is given as Rs. 736, and the discount is 30%.

**Formula for Selling Price (SP):**
\[ SP = MP - (Discount \% \times MP) \]

**Calculation:**
\[ Discount = 30\% \text{ of } 736 = \frac{30}{100} \times 736 = 220.8 \]
\[ SP = 736 - 220.8 = 515.2 \]

### Step 2: Calculate the Profit
The cost price (CP) of the article is given as Rs. 460.

**Profit Calculation:**
\[ Profit = SP - CP \]
\[ Profit = 515.2 - 460 = 55.2 \]

### Step 3: Calculate the Gain Percentage (x%)
The gain percentage (x%) is calculated using the formula:
\[ Gain \% = \left( \frac{Profit}{CP} \right) \times 100 \]

**Calculation:**
\[ Gain \% = \left( \frac{55.2}{460} \right) \times 100 \]
\[ Gain \% = 0.12 \times 100 = 12\% \]

### Conclusion
The value of x is **12%**.

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