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

Options

A. `2.8%`
B. `4 (1)/(6) %`
C. `4.16%`
D. `3 (1)/(3) %`

Answer

To solve the problem of finding the gain percent of a dishonest dealer who sells goods at cost price but uses a weight of 960 grams instead of 1000 grams, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Selling Price and Cost Price**:
- The dealer sells the goods at the cost price of 1 kg (1000 grams).
- Therefore, the selling price (SP) for 1 kg is the cost price (CP) of 1 kg.

\[ SP = CP = 1000 \text{ (Assuming the cost price for 1 kg is 1000 units of currency)} \]

2. **Determine the Actual Weight Sold**:
- The dealer uses a weight of 960 grams instead of 1000 grams.
- This means when he sells 1 kg, he is actually giving only 960 grams.

3. **Calculate the Cost Price for 960 grams**:
- Since the cost price for 1 kg (1000 grams) is 1000 units, the cost price for 960 grams can be calculated as follows:

\[ CP \text{ for 960 grams} = \left(\frac{960}{1000}\right) \times 1000 = 960 \text{ units} \]

4. **Calculate the Gain**:
- The gain can be calculated as the difference between the selling price and the cost price for the actual weight sold.

\[ \text{Gain} = SP - CP \text{ for 960 grams} = 1000 - 960 = 40 \text{ units} \]

5. **Calculate Gain Percent**:
- Gain percent is calculated using the formula:

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

Substituting the values we have:

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

6. **Simplify the Calculation**:
- Now, simplify the fraction:

\[ \text{Gain Percent} = \left(\frac{40 \times 100}{960}\right) = \frac{4000}{960} \]

- Dividing both the numerator and denominator by 40:

\[ \text{Gain Percent} = \frac{100}{24} \approx 4.1667 \]

- To express this as a percentage:

\[ \text{Gain Percent} = \frac{25}{6} \text{ percent} \approx 4.17 \text{ percent} \]

### Final Answer:
The gain percent of the dishonest dealer is approximately **4.17%** or **\(\frac{25}{6}\%\)**.