A dishonest dealer professes to sell his goods at cost price but he uses a weight of 900 gm in place of 1 kg.
Find his gain per cent.

Options

A. `(100)/(3)%`
B. `(100)/(9)%`
C. `(200)/(3)%`
D. `(200)/(9)%`

Answer

To find the gain percentage of the dishonest dealer who uses a weight of 900 grams instead of 1 kilogram, we can follow these steps:

### Step 1: Understand the true weight and false weight
- The true weight of 1 kilogram is 1000 grams.
- The dealer uses a false weight of 900 grams instead of 1000 grams.

### Step 2: Calculate the error in weight
- The error in weight can be calculated as:
\[ \text{Error} = \text{True Weight} - \text{False Weight} = 1000 \, \text{grams} - 900 \, \text{grams} = 100 \, \text{grams} \]

### Step 3: Calculate the gain percentage
- The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Error}}{\text{True Weight} - \text{Error}} \right) \times 100 \]
- Substitute the values:
\[ \text{Gain Percentage} = \left( \frac{100 \, \text{grams}}{1000 \, \text{grams} - 100 \, \text{grams}} \right) \times 100 \]
\[ = \left( \frac{100}{900} \right) \times 100 \]

### Step 4: Simplify the calculation
- Simplifying the fraction:
\[ = \frac{100}{900} \times 100 = \frac{10000}{900} \]
- Reducing the fraction:
\[ = \frac{1000}{90} = \frac{100}{9} \]

### Step 5: Final result
- Therefore, the gain percentage is:
\[ \text{Gain Percentage} = \frac{100}{9} \% \]

### Final Answer:
The gain percentage of the dishonest dealer is \(\frac{100}{9} \%\).

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