A trader bought a bag of 40 kg of basmati rice at Rs . 125 per kg and another bag of 60 kg at Rs. 150 per kg . He sold the entire stock at a profit of 20% . Find the selling price per kg .
A. Rs. 152
B. Rs.158
C. Rs. 168
D. Rs.172

Options

A. C
B. A
C. B
D. D

Answer

To solve the problem step by step, we will first calculate the total cost of the rice, then determine the selling price after applying the profit percentage.

### Step 1: Calculate the total cost of the first bag of rice
The first bag weighs 40 kg and costs Rs. 125 per kg.
\[ \text{Cost of first bag} = 40 \text{ kg} \times 125 \text{ Rs/kg} = 5000 \text{ Rs} \]

### Step 2: Calculate the total cost of the second bag of rice
The second bag weighs 60 kg and costs Rs. 150 per kg.
\[ \text{Cost of second bag} = 60 \text{ kg} \times 150 \text{ Rs/kg} = 9000 \text{ Rs} \]

### Step 3: Calculate the total cost of both bags
Now, we will sum the costs of both bags to find the total cost.
\[ \text{Total cost} = \text{Cost of first bag} + \text{Cost of second bag} = 5000 \text{ Rs} + 9000 \text{ Rs} = 14000 \text{ Rs} \]

### Step 4: Calculate the total weight of the rice
The total weight of the rice is the sum of the weights of both bags.
\[ \text{Total weight} = 40 \text{ kg} + 60 \text{ kg} = 100 \text{ kg} \]

### Step 5: Calculate the selling price after a 20% profit
To find the selling price, we first calculate the profit amount and then add it to the total cost.
\[ \text{Profit} = 20\% \text{ of Total Cost} = \frac{20}{100} \times 14000 \text{ Rs} = 2800 \text{ Rs} \]
\[ \text{Selling Price} = \text{Total Cost} + \text{Profit} = 14000 \text{ Rs} + 2800 \text{ Rs} = 16800 \text{ Rs} \]

### Step 6: Calculate the selling price per kg
Now, we divide the total selling price by the total weight to find the selling price per kg.
\[ \text{Selling Price per kg} = \frac{\text{Total Selling Price}}{\text{Total Weight}} = \frac{16800 \text{ Rs}}{100 \text{ kg}} = 168 \text{ Rs/kg} \]

### Final Answer
The selling price per kg is Rs. 168.