Calculating Rice Mixture Profit Percent

This problem involves calculating the profit percentage when a trader mixes two types of rice and sells the mixture.

1. Determine Total Quantity

First, find the total weight of the rice mixture by adding the quantities of the two varieties:

Total Quantity = Quantity of Rice 1 + Quantity of Rice 2

Total Quantity = 245 kg + 255 kg = 500 kg

2. Calculate Total Cost Price (CP)

Both rice varieties are mixed at the same cost price of Rs. 155 per kg. Therefore, the cost price of the entire mixture is:

Total CP = Total Quantity $\times$ Cost Price per kg

Total CP = 500 kg $\times$ Rs. 155/kg = Rs. 77500

3. Calculate Total Selling Price (SP)

The mixture is sold at Rs. 186 per kg. Calculate the total selling price:

Total SP = Total Quantity $\times$ Selling Price per kg

Total SP = 500 kg $\times$ Rs. 186/kg = Rs. 93000

4. Calculate Profit

Profit is the difference between the total selling price and the total cost price:

Profit = Total SP - Total CP

Profit = Rs. 93000 - Rs. 77500 = Rs. 15500

5. Calculate Profit Percent

The profit percentage is calculated using the formula:

Profit \% = \(\left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100\)

Profit \% = \(\left( \frac{15500}{77500} \right) \times 100\)

Profit \% = \(\left( \frac{155}{775} \right) \times 100\)

Profit \% = \(\frac{1}{5} \times 100\)

Profit \% = 20\%

Alternatively, since the cost price per kg is the same for both types of rice (Rs. 155/kg), the cost price of the mixture is also Rs. 155/kg. The selling price is Rs. 186/kg.

Profit per kg = SP per kg - CP per kg = Rs. 186 - Rs. 155 = Rs. 31

Profit \% = \(\left( \frac{\text{Profit per kg}}{\text{CP per kg}} \right) \times 100\)

Profit \% = \(\left( \frac{31}{155} \right) \times 100 = \frac{1}{5} \times 100 = 20\%\)