At what per cent above the cost price must an articles be marked, so as to gain `17%` after allowing a discount of `10%`?

Options

A. `34%`
B. `70%`
C. `30%`
D. `27%`

Answer

To solve the problem of determining the percentage above the cost price at which an article must be marked to achieve a 17% gain after allowing a 10% discount, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the marked price (MP) that is a certain percentage above the cost price (CP) so that after giving a discount of 10%, we still achieve a profit of 17%.

2. **Set Up the Equations**:
- Let the cost price (CP) be 100 (for simplicity).
- The desired selling price (SP) after a 17% gain on the cost price is:
\[ SP = CP + 17\% \text{ of } CP = 100 + 17 = 117 \]

3. **Account for the Discount**:
- The selling price (SP) is also related to the marked price (MP) after applying the discount of 10%. Therefore, we can express the selling price as:
\[ SP = MP - 10\% \text{ of } MP = MP - 0.1 \times MP = 0.9 \times MP \]

4. **Equate the Selling Prices**:
- Since both expressions represent the selling price, we can set them equal to each other:
\[ 0.9 \times MP = 117 \]

5. **Solve for Marked Price (MP)**:
- To find MP, divide both sides by 0.9:
\[ MP = \frac{117}{0.9} = 130 \]

6. **Calculate the Marked Price Percentage Above Cost Price**:
- Now, we find the percentage increase from the cost price to the marked price:
\[ \text{Percentage Increase} = \left(\frac{MP - CP}{CP}\right) \times 100 = \left(\frac{130 - 100}{100}\right) \times 100 = 30\% \]

### Final Answer:
The article must be marked at **30% above the cost price**.

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