A dishonest dealer professes to sell his goods at cost price, but he uses a weight of `960` grams for `1 kg`. Find his gain percent.

Options

A. `4.557%`
B. `4.167%`
C. `3167%`
D. `2.567%`

Answer

To solve the problem step by step, we will calculate the gain percent of the dishonest dealer who uses a weight of 960 grams instead of 1 kg (1000 grams).

### Step 1: Identify the True Value and False Value
- **True Value**: This is the actual weight that should be sold, which is 1 kg = 1000 grams.
- **False Value**: This is the weight that the dealer actually sells, which is 960 grams.

### Step 2: Calculate the Error
- **Error**: This is the difference between the true value and the false value.

\[ \text{Error} = \text{True Value} - \text{False Value} = 1000 \text{ grams} - 960 \text{ grams} = 40 \text{ grams} \]

### Step 3: Use the Gain Percent Formula
The formula for gain percent is given by:

\[ \text{Gain Percent} = \left( \frac{\text{Error}}{\text{False Value}} \right) \times 100 \]

### Step 4: Substitute the Values into the Formula
- Substitute the error (40 grams) and the false value (960 grams) into the formula:

\[ \text{Gain Percent} = \left( \frac{40}{960} \right) \times 100 \]

### Step 5: Simplify the Calculation
- First, simplify the fraction:

\[ \frac{40}{960} = \frac{1}{24} \]

- Now, multiply by 100:

\[ \text{Gain Percent} = \left( \frac{1}{24} \right) \times 100 = \frac{100}{24} = 4.1667 \text{ (approximately)} \]

### Step 6: Convert to a Percentage
- To express it as a percentage:

\[ \text{Gain Percent} \approx 4.17\% \]

### Final Result
The gain percent of the dishonest dealer is approximately **4.17%**.

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