The marked price of an article is 30% higher than the cost price. If a tender sells the articles allowing 10% discount to customer, then the gain percent will be.

Options

A. 17
B. 20
C. 19
D. 15

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between Cost Price (CP) and Marked Price (MP)
The marked price (MP) is given to be 30% higher than the cost price (CP). This can be expressed mathematically as:
\[ MP = CP + 0.30 \times CP = 1.30 \times CP \]

### Step 2: Calculate the Selling Price (SP) after discount
The article is sold at a 10% discount on the marked price. The selling price (SP) can be calculated as:
\[ SP = MP - (10\% \text{ of } MP) \]
This can be rewritten as:
\[ SP = MP \times (1 - 0.10) = MP \times 0.90 \]
Substituting the expression for MP from Step 1:
\[ SP = (1.30 \times CP) \times 0.90 = 1.17 \times CP \]

### Step 3: Calculate the Gain
The gain can be calculated by subtracting the cost price from the selling price:
\[ \text{Gain} = SP - CP = (1.17 \times CP) - CP = 0.17 \times CP \]

### Step 4: Calculate the Gain Percent
To find the gain percent, we use the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the gain from Step 3:
\[ \text{Gain Percent} = \left( \frac{0.17 \times CP}{CP} \right) \times 100 = 17\% \]

### Conclusion
Thus, the gain percent when selling the article is **17%**.

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