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

Options

A. 0.34
B. 0.7
C. 0.3
D. 0.27

Answer

To solve the problem, we need to find the percentage above the cost price at which an article must be marked in order to achieve a 17% profit after allowing a 10% discount.

### Step-by-Step Solution:

1. **Define the Cost Price (CP)**:
Let's assume the cost price (CP) of the article is \(100\) (this simplifies calculations).

2. **Calculate the Selling Price (SP)**:
Since we want a profit of \(17\%\), the selling price (SP) can be calculated as follows:
\[ SP = CP + 17\% \text{ of } CP = 100 + 17 = 117 \]

3. **Understand the Discount**:
We are given that a discount of \(10\%\) is allowed on the marked price (MP). After applying this discount, the selling price should still be \(117\).

4. **Set Up the Equation for Marked Price (MP)**:
If the marked price is \(X\), after a \(10\%\) discount, the selling price becomes:
\[ SP = MP - 10\% \text{ of } MP = X - 0.1X = 0.9X \]
Therefore, we can set up the equation:
\[ 0.9X = 117 \]

5. **Solve for Marked Price (MP)**:
To find \(X\), rearrange the equation:
\[ X = \frac{117}{0.9} = 130 \]

6. **Calculate the Percentage Above Cost Price**:
Now, we need to find out how much \(X\) (the marked price) is above the cost price:
\[ \text{Difference} = X - CP = 130 - 100 = 30 \]
To find the percentage above the cost price:
\[ \text{Percentage} = \left(\frac{\text{Difference}}{CP}\right) \times 100 = \left(\frac{30}{100}\right) \times 100 = 30\% \]

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

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