The marked price of a table is 50% more than its cost price. What discount per cent should be offered by the shopkeeper to sell his table at no profit or no loss ?

Options

A. 66.66
B. 33.33
C. 40
D. 25

Answer

To solve the problem step by step, we will first define the terms and then calculate the required discount percentage.

### Step 1: Define the Cost Price (CP)
Let the cost price (CP) of the table be \( CP = x \).

### Step 2: Calculate the Marked Price (MP)
Since the marked price is 50% more than the cost price, we can express the marked price as:
\[ MP = CP + 50\% \text{ of } CP \]
\[ MP = x + \frac{50}{100} \times x = x + 0.5x = 1.5x \]

### Step 3: Determine the Selling Price (SP) for No Profit or No Loss
To sell the table at no profit or no loss, the selling price (SP) must be equal to the cost price (CP):
\[ SP = CP = x \]

### Step 4: Calculate the Discount
The discount can be calculated using the formula:
\[ \text{Discount} = MP - SP \]
Substituting the values we have:
\[ \text{Discount} = 1.5x - x = 0.5x \]

### Step 5: Calculate the Discount Percentage
The discount percentage can be calculated using the formula:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{MP} \right) \times 100 \]
Substituting the values:
\[ \text{Discount Percentage} = \left( \frac{0.5x}{1.5x} \right) \times 100 \]
The \( x \) cancels out:
\[ \text{Discount Percentage} = \left( \frac{0.5}{1.5} \right) \times 100 = \frac{1}{3} \times 100 \approx 33.33\% \]

### Final Answer
The shopkeeper should offer a discount of approximately **33.33%** to sell the table at no profit or no loss.

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