A trader sells wheat at 20% profit and uses weight 20% less than the actual measure.His gain percent is

Options

A. `35%`
B. `38%`
C. `48%`
D. `50%`

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the Given Information
The trader sells wheat at a profit of 20% and uses 20% less weight than the actual measure.

### Step 2: Assume a Cost Price (CP)
Let's assume the cost price (CP) of 1000 grams of wheat is Rs 1000.

### Step 3: Calculate the Selling Price (SP)
Since the trader sells at a profit of 20%, we can calculate the selling price (SP) as follows:
\[ SP = CP + (Profit \% \times CP) = CP \times \left(1 + \frac{20}{100}\right) \]
\[ SP = 1000 \times \frac{120}{100} = 1200 \text{ Rs} \]

### Step 4: Calculate the Actual Weight Sold
The trader uses 20% less weight. Therefore, the actual weight sold is:
\[ \text{Actual Weight} = 1000 \times (1 - 0.20) = 1000 \times 0.80 = 800 \text{ grams} \]

### Step 5: Calculate the Cost Price of the Actual Weight Sold
Since the cost price of 1000 grams is Rs 1000, the cost price of 800 grams is:
\[ CP_{\text{actual}} = \frac{800}{1000} \times 1000 = 800 \text{ Rs} \]

### Step 6: Calculate the Profit
Now, we can calculate the profit made by the trader:
\[ \text{Profit} = SP - CP_{\text{actual}} = 1200 - 800 = 400 \text{ Rs} \]

### Step 7: Calculate the Profit Percentage
Finally, we need to calculate the profit percentage based on the cost price of the actual weight sold:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP_{\text{actual}}}\right) \times 100 = \left(\frac{400}{800}\right) \times 100 = 50\% \]

### Final Answer
The trader's gain percentage is **50%**.

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