A dishonest dealer professes to sell his goods at the cost price but uses a false weight of 850 g instead of 1 kg. His gain percent is

Options

A. `17 (12)/(17)%`
B. `17 (11)/(17)%`
C. `71 (11)/(17) %`
D. `11 (11)/(17)%`

Answer

To solve the problem of finding the gain percentage of a dishonest dealer who sells goods at the cost price but uses a false weight of 850 g instead of 1 kg, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Weights**:
- True weight (actual weight of goods) = 1 kg = 1000 g
- False weight (weight used by the dealer) = 850 g

2. **Calculate the Gain in Weight**:
- Gain in weight = True weight - False weight
- Gain in weight = 1000 g - 850 g = 150 g

3. **Use the Gain Percentage Formula**:
- Gain Percentage = (Gain in weight / False weight) × 100
- Here, Gain in weight = 150 g and False weight = 850 g

4. **Substitute the Values into the Formula**:
- Gain Percentage = (150 g / 850 g) × 100

5. **Simplify the Calculation**:
- Gain Percentage = (150 / 850) × 100
- Gain Percentage = (150 / 850) × 100 = (15 / 85) × 100

6. **Further Simplify**:
- Divide both the numerator and denominator by 5:
- Gain Percentage = (3 / 17) × 100

7. **Calculate the Final Gain Percentage**:
- Gain Percentage = (3 × 100) / 17
- Gain Percentage = 300 / 17

8. **Perform the Division**:
- Gain Percentage ≈ 17.6471%

9. **Express as a Fraction**:
- Gain Percentage = 17 + (11/17)%

### Final Answer:
The gain percentage of the dishonest dealer is approximately **17 11/17%**.