At what per cent above the cost price, must a shop-keeper marks his goods so that he gains 20% even after giving a discount of 10% on the marked price?

Options

A. 0.25
B. 0.3
C. 33 `1/3` %
D. 37 `1/2` %

Answer

To solve the problem step-by-step, we need to determine the percentage above the cost price (CP) at which a shopkeeper must mark his goods to achieve a 20% profit after giving a 10% discount on the marked price (MP).

### Step 1: Define the Cost Price
Let the cost price (CP) of the goods be \(100\) (for simplicity).

### Step 2: Calculate the Selling Price for 20% Profit
To find the selling price (SP) that gives a 20% profit on the cost price:
\[ SP = CP + (20\% \text{ of } CP) = 100 + (0.20 \times 100) = 100 + 20 = 120 \]

### Step 3: Calculate the Marked Price Considering the Discount
The shopkeeper gives a discount of 10% on the marked price (MP). Let the marked price be \(MP\). After applying a 10% discount, the selling price can be expressed as:
\[ SP = MP - (10\% \text{ of } MP) = MP - (0.10 \times MP) = 0.90 \times MP \]

### Step 4: Set the Selling Price Equal to the Calculated Selling Price
Since we have calculated the selling price (SP) to be \(120\), we can set up the equation:
\[ 0.90 \times MP = 120 \]

### Step 5: Solve for Marked Price
To find \(MP\), we rearrange the equation:
\[ MP = \frac{120}{0.90} = \frac{1200}{90} = \frac{1200 \div 30}{90 \div 30} = \frac{40}{3} \approx 133.33 \]

### Step 6: Calculate the Percentage Increase from Cost Price to Marked Price
Now, we need to find out how much more the marked price is compared to the cost price in percentage terms:
\[ \text{Percentage Increase} = \left( \frac{MP - CP}{CP} \right) \times 100 = \left( \frac{133.33 - 100}{100} \right) \times 100 \]
\[ = \left( \frac{33.33}{100} \right) \times 100 = 33.33\% \]

### Conclusion
Thus, the shopkeeper must mark his goods at **33.33%** above the cost price to achieve a 20% profit after giving a 10% discount.

---