Alok bought 25 kg and 35 kg of rice at the rate of Rs. 7 per kg. He mixed the two and sold the mixture at the rate two and sold the mixture at the rate of Rs. `6.75` per kg. What was his gain or loss in this transaction ?

Options

A. Rs. `16.00` gain
B. Rs. `16.00` loss
C. Rs. `20.00` gain
D. None of these

Answer

To solve the problem step by step, we will calculate the cost price (CP) of the rice mixture, the selling price (SP) of the mixture, and then determine the gain or loss.

### Step 1: Calculate the Cost Price (CP) of the Rice Mixture
Alok bought:
- 25 kg of rice at Rs. 7 per kg
- 35 kg of rice at Rs. 7 per kg

First, we calculate the total cost for each quantity of rice:

1. Cost of 25 kg of rice:
\[ \text{Cost of 25 kg} = 25 \, \text{kg} \times 7 \, \text{Rs/kg} = 175 \, \text{Rs} \]

2. Cost of 35 kg of rice:
\[ \text{Cost of 35 kg} = 35 \, \text{kg} \times 7 \, \text{Rs/kg} = 245 \, \text{Rs} \]

Now, we add these two amounts to find the total cost price of the mixture:
\[ \text{Total CP} = 175 \, \text{Rs} + 245 \, \text{Rs} = 420 \, \text{Rs} \]

### Step 2: Calculate the Selling Price (SP) of the Rice Mixture
The total weight of the mixture is:
\[ \text{Total weight} = 25 \, \text{kg} + 35 \, \text{kg} = 60 \, \text{kg} \]

Alok sold the mixture at Rs. 6.75 per kg. Therefore, the total selling price is:
\[ \text{Total SP} = 60 \, \text{kg} \times 6.75 \, \text{Rs/kg} = 405 \, \text{Rs} \]

### Step 3: Calculate Gain or Loss
Now, we can find the gain or loss by subtracting the total cost price from the total selling price:
\[ \text{Gain/Loss} = \text{Total SP} - \text{Total CP} = 405 \, \text{Rs} - 420 \, \text{Rs} = -15 \, \text{Rs} \]

Since the result is negative, it indicates a loss.

### Step 4: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{15}{420} \right) \times 100 \approx 3.57\% \]

### Final Answer
Alok incurred a loss of Rs. 15, which is approximately 3.57%.

---