A shopkeeper reduces the price of his goods by 50% at the time of sale. Initially the price was fixed to get a profit of 25% on selling price after allowing 10% cash discount. Find out his approximate percentage of profit or loss.

Options

A. 26%loss
B. 28%profit
C. 30%loss
D. 26%profit

Answer

To solve the problem step by step, we will break down the information provided and calculate the required values.

### Step 1: Understand the Selling Price after Discount
The shopkeeper gives a 10% cash discount on the marked price (MP). If we assume the marked price is 100, then after a 10% discount, the selling price (SP) can be calculated as:
\[ SP = MP - (10\% \text{ of } MP) = 100 - 10 = 90 \]

**Hint:** Remember that a discount reduces the price, so calculate the selling price by subtracting the discount from the marked price.

### Step 2: Calculate the Cost Price based on Profit
The shopkeeper aims for a profit of 25% on the selling price. Therefore, the cost price (CP) can be calculated using the formula:
\[ CP = \frac{SP \times 100}{125} \]
Substituting the selling price we found:
\[ CP = \frac{90 \times 100}{125} = \frac{9000}{125} = 72 \]

**Hint:** To find the cost price when you know the selling price and the desired profit percentage, use the formula that relates SP, CP, and profit percentage.

### Step 3: Calculate the Selling Price during Sale
During the sale, the shopkeeper reduces the price by 50%. Therefore, the new selling price during the sale (let's call it SP_sale) is:
\[ SP_{sale} = \frac{MP}{2} = \frac{100}{2} = 50 \]

**Hint:** A 50% reduction means you take half of the marked price.

### Step 4: Determine Profit or Loss
Now, we need to compare the selling price during the sale with the cost price to determine profit or loss.
- Selling Price during Sale = 50
- Cost Price = 72

Since the selling price (50) is less than the cost price (72), the shopkeeper incurs a loss.

**Hint:** To identify profit or loss, compare the selling price with the cost price.

### Step 5: Calculate the Amount of Loss
The loss can be calculated as:
\[ \text{Loss} = CP - SP_{sale} = 72 - 50 = 22 \]

**Hint:** Loss is calculated by subtracting the selling price from the cost price when the selling price is lower.

### Step 6: Calculate the Percentage of Loss
The percentage loss can be calculated using the formula:
\[ \text{Percentage Loss} = \left(\frac{\text{Loss}}{CP}\right) \times 100 = \left(\frac{22}{72}\right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Loss} = \frac{2200}{72} \approx 30.56 \approx 30\% \]

**Hint:** To find the percentage loss, divide the loss by the cost price and multiply by 100.

### Final Answer
The approximate percentage of loss is **30%**.