A shopkeeper blends two varieties of coffee beans—the first priced at ₹150 per kg and the second at ₹200 per kg—in a ratio of 2 : 3. If the combined mixture is sold at a rate of ₹180 per kg, determine the overall profit or loss percentage.

Correct Answer: no loss, no gain

Let us solve this problem step-by-step to find the overall profit or loss percentage.

Step 1: Calculate the total cost price of the blended mixture.

The shopkeeper blends two varieties of coffee beans in the ratio of 2 : 3.

For ease of calculation, let the quantity of the first variety of coffee beans be 2 kg and the quantity of the second variety be 3 kg.

Total quantity of the mixture = 2 kg + 3 kg = 5 kg.

The price of the first variety = ₹150 per kg.

Cost of 2 kg of the first variety = $2\times 150=300$ rupees.

The price of the second variety = ₹200 per kg.

Cost of 3 kg of the second variety = $3\times 200=600$ rupees.

Total Cost Price (CP) of the 5 kg mixture:

$\text{Total CP}=300+600=900$ rupees.

Step 2: Calculate the total selling price of the mixture.

The mixture is sold at a rate of ₹180 per kg.

Total Selling Price (SP) of the 5 kg mixture:

$\text{Total SP}=5\times 180=900$ rupees.

Step 3: Determine the profit or loss.

Comparing the Total Cost Price and Total Selling Price:

$\text{Total Cost Price (CP)}=900$ rupees.

$\text{Total Selling Price (SP)}=900$ rupees.

Since the Total Cost Price is equal to the Total Selling Price ($\text{CP}=\text{SP}$), there is no loss, no gain.