A trader buys rice from a farmer using faulty weight at a rate which is same as his selling price in the market. However, his 1kg weight 1050g. Find his gain per cent.

Options

A. 7
B. `5.5`
C. 15
D. 5

Answer

To solve the problem, we need to determine the trader's gain percentage based on the faulty weight he uses when buying rice. Here’s a step-by-step solution:

### Step 1: Understand the faulty weight
The trader uses a weight that is supposed to be 1 kg (1000 grams) but is actually 1050 grams. This means that when he claims to buy 1 kg of rice, he is actually getting more rice than he pays for.

### Step 2: Calculate the effective cost price (CP)
Let’s assume the cost price of rice is ₹1 per gram. Therefore, for 1000 grams (1 kg), the cost price would be:
\[ \text{CP for 1000g} = 1000 \text{ grams} \times ₹1/\text{gram} = ₹1000 \]

### Step 3: Determine the actual quantity of rice received
When the trader buys what he claims to be 1 kg of rice, he actually receives 1050 grams.

### Step 4: Calculate the selling price (SP)
Since the trader sells the rice at the same rate as the cost price, the selling price for the 1050 grams of rice is:
\[ \text{SP for 1050g} = 1050 \text{ grams} \times ₹1/\text{gram} = ₹1050 \]

### Step 5: Calculate the gain
The gain made by the trader can be calculated as:
\[ \text{Gain} = \text{SP} - \text{CP} = ₹1050 - ₹1000 = ₹50 \]

### Step 6: Calculate the gain percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{₹50}{₹1000} \right) \times 100 = 5\% \]

### Final Answer
The trader's gain percentage is **5%**.

---