A shopkeeper uses 960 gram against a weight of One KG. Find his Gain percentage

Answer

To solve the problem of finding the gain percentage for the shopkeeper who uses 960 grams instead of 1 kilogram (1000 grams), we can follow these steps:

### Step 1: Identify the Cost Price
The cost price (CP) for the shopkeeper is the weight he actually uses, which is 960 grams.

### Step 2: Identify the Selling Price
The selling price (SP) is the weight he claims to sell, which is 1 kilogram (1000 grams).

### Step 3: Calculate the Error in Weight
The error in weight is the difference between the claimed weight and the actual weight used:
\[ \text{Error} = \text{SP} - \text{CP} = 1000 \text{ grams} - 960 \text{ grams} = 40 \text{ grams} \]

### Step 4: Calculate the Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Error}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{40 \text{ grams}}{960 \text{ grams}} \right) \times 100 \]

### Step 5: Simplify the Calculation
Calculating the fraction:
\[ \frac{40}{960} = \frac{1}{24} \]
Now, substituting this back into the gain percentage formula:
\[ \text{Gain Percentage} = \left( \frac{1}{24} \right) \times 100 = \frac{100}{24} \approx 4.1667 \text{ (or } 4 \frac{1}{6} \text{ percent)} \]

### Final Answer
The gain percentage for the shopkeeper is approximately \( 4 \frac{1}{6} \% \).

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