A dishonest dealer professes to sell his goods at cost price but he uses a weight of 920g for 1kg weight. Find his gain per cent.

Options

A. `7(16)/(23)%`
B. `8(16)/(23)%`
C. `5(16)/(23)%`
D. `3(16)/(23)%`

Answer

To solve the problem of finding the gain percentage of a dishonest dealer who uses a weight of 920g instead of 1kg (1000g) while professing to sell at cost price, we can follow these steps:

### Step 1: Understand the situation
The dealer claims to sell 1 kg of goods at the cost price, but he actually sells only 920 grams. This means he is gaining from the difference in weight.

### Step 2: Calculate the weight difference
The difference in weight is:
\[ \text{Weight difference} = 1000g - 920g = 80g \]

### Step 3: Calculate the gain
The gain is the weight difference, which is 80 grams. Since the dealer sells 920 grams as if it were 1000 grams, he effectively gains the value of the 80 grams.

### Step 4: Calculate the gain percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{Actual Weight}}\right) \times 100 \]
In this case, the gain is 80 grams and the actual weight (which he claims to sell) is 1000 grams.

Substituting the values:
\[ \text{Gain Percentage} = \left(\frac{80g}{1000g}\right) \times 100 \]

### Step 5: Simplify the calculation
\[ \text{Gain Percentage} = \left(\frac{80}{1000}\right) \times 100 = 8\% \]

### Conclusion
The gain percentage of the dishonest dealer is **8%**.

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