How much per cent more than the cost price should a shopkeeper marks his goods so that after allowing a discount of 20% on the marked price, he gains 10%?

Answer

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

### Step 1: Define Variables
Let the Cost Price (CP) of the goods be \( x \).

### Step 2: Calculate Selling Price for Profit
The shopkeeper wants to gain a profit of 10%. Therefore, the Selling Price (SP) can be calculated as:
\[ SP = CP + 10\% \text{ of } CP = x + 0.1x = 1.1x \]

### Step 3: Calculate Selling Price after Discount
The shopkeeper gives a discount of 20% on the Marked Price (MP). After the discount, the Selling Price (SP) is:
\[ SP = MP - 20\% \text{ of } MP = MP - 0.2 \times MP = 0.8 \times MP \]

### Step 4: Set the Selling Prices Equal
Since both expressions for Selling Price represent the same value, we can set them equal to each other:
\[ 0.8 \times MP = 1.1x \]

### Step 5: Solve for Marked Price
To find the Marked Price (MP), rearrange the equation:
\[ MP = \frac{1.1x}{0.8} \]
\[ MP = \frac{11x}{8} \]

### Step 6: Calculate the Increase in Price
Now, we need to find out how much more the Marked Price is compared to the Cost Price. The increase in price is:
\[ MP - CP = \frac{11x}{8} - x = \frac{11x}{8} - \frac{8x}{8} = \frac{3x}{8} \]

### Step 7: Calculate the Percentage Increase
To find the percentage increase over the Cost Price, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{MP - CP}{CP} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Increase} = \left( \frac{\frac{3x}{8}}{x} \right) \times 100 = \frac{3}{8} \times 100 = 37.5\% \]

### Final Answer
The shopkeeper should mark his goods **37.5% more** than the cost price.

---