A shopkeeper marked the sell ing price of his goods in such a way that after giving a discount of 10% he gains 17%. How much per cent above the cost price is the marked price?

Options

A. 0.36
B. 0.27
C. 0.3
D. 0.4

Answer

To solve the problem step by step, we will use the information given about the selling price (SP), cost price (CP), and marked price (MP).

### Step 1: Understand the given information
- The shopkeeper gives a discount of 10% on the marked price (MP).
- After giving this discount, he gains 17% on the cost price (CP).

### Step 2: Define the cost price
Let the cost price (CP) be represented as \( CP = 100 \) (for simplicity in percentage calculations).

### Step 3: Calculate the selling price using the gain
Since the shopkeeper gains 17% on the cost price:
\[ SP = CP + \text{Gain} = 100 + 17 = 117 \]

### Step 4: Relate the selling price to the marked price
The selling price (SP) is also related to the marked price (MP) after applying the discount. The discount given is 10% of the marked price:
\[ SP = MP - (10\% \text{ of } MP) = MP - 0.1 \cdot MP = 0.9 \cdot MP \]

### Step 5: Set up the equation
From the previous steps, we have:
\[ 0.9 \cdot MP = 117 \]

### Step 6: Solve for the marked price
To find the marked price (MP), we rearrange the equation:
\[ MP = \frac{117}{0.9} = 130 \]

### Step 7: Calculate how much the marked price is above the cost price
Now we need to find out how much the marked price is above the cost price:
\[ \text{Difference} = MP - CP = 130 - 100 = 30 \]

### Step 8: Calculate the percentage above the cost price
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 marked price is 30% above the cost price.

---