A dishonest shopkeeper claims to sell his goods at cost price but uses a weight of 800 gm in place of the standard 1 kg weight. What is his gain per cent?

Answer

To find the gain percentage of the dishonest shopkeeper who uses a weight of 800 grams instead of the standard 1 kg (1000 grams), we can follow these steps:

### Step 1: Identify the error in weight
The shopkeeper claims to sell 1 kg (1000 grams) but actually sells only 800 grams. Therefore, the error in weight is:
\[ \text{Error} = \text{Actual weight} - \text{Weight used} = 1000 \text{ grams} - 800 \text{ grams} = 200 \text{ grams} \]

### Step 2: Use the formula for profit percentage
The formula for profit percentage when dealing with false weight is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Error}}{\text{Actual Value}} \right) \times 100 \]
In this case, the actual value is the weight that the shopkeeper should have sold, which is 800 grams.

### Step 3: Substitute the values into the formula
Now, substituting the values into the formula:
\[ \text{Profit Percentage} = \left( \frac{200 \text{ grams}}{800 \text{ grams}} \right) \times 100 \]

### Step 4: Simplify the fraction
Calculating the fraction:
\[ \frac{200}{800} = \frac{1}{4} \]

### Step 5: Calculate the profit percentage
Now, substituting back into the profit percentage formula:
\[ \text{Profit Percentage} = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Final Answer
The gain percentage of the dishonest shopkeeper is **25%**.

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