A shopkeeper marks price of his goods in such a way that after allowing a discount of 10%, he gains 26%. How much percent above the cost price is the marked price ?

Options

A. `36%`
B. `38%`
C. `40%`
D. `28%`

Answer

To solve the problem, we need to find out how much percent above the cost price the marked price is, given that the shopkeeper allows a discount of 10% and gains a profit of 26%.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Discount = 10%
- Profit = 26%

2. **Set Up the Formula:**
The relationship between cost price (CP), marked price (MP), discount, and profit can be expressed using the formula:
\[ \frac{100 - \text{Discount}}{100 + \text{Profit}} = \frac{\text{CP}}{\text{MP}} \]

3. **Substitute the Values:**
Substitute the discount and profit percentages into the formula:
\[ \frac{100 - 10}{100 + 26} = \frac{\text{CP}}{\text{MP}} \]
This simplifies to:
\[ \frac{90}{126} = \frac{\text{CP}}{\text{MP}} \]

4. **Simplify the Ratio:**
Now, simplify the fraction:
\[ \frac{90}{126} = \frac{15}{21} = \frac{5}{7} \]
Thus, we have:
\[ \frac{\text{CP}}{\text{MP}} = \frac{5}{7} \]

5. **Express Marked Price in Terms of Cost Price:**
From the ratio, we can express the marked price in terms of the cost price:
\[ \text{MP} = \frac{7}{5} \times \text{CP} \]

6. **Calculate the Percentage Increase:**
To find out how much percent the marked price is above the cost price, we calculate:
\[ \text{Percentage Increase} = \left( \frac{\text{MP} - \text{CP}}{\text{CP}} \right) \times 100 \]
Substitute the expression for MP:
\[ \text{Percentage Increase} = \left( \frac{\frac{7}{5} \text{CP} - \text{CP}}{\text{CP}} \right) \times 100 \]
Simplifying this gives:
\[ = \left( \frac{\frac{7}{5} \text{CP} - \frac{5}{5} \text{CP}}{\text{CP}} \right) \times 100 = \left( \frac{\frac{2}{5} \text{CP}}{\text{CP}} \right) \times 100 = \frac{2}{5} \times 100 = 40\% \]

### Final Answer:
The marked price is **40% above the cost price**.