Question

A dry fruit seller purchased 3 kinds of nuts at the rate of 100/kg, 80/kg and 60/kg. He then mixed them, respectively, in the ratio 3 : 4 : 5 by weight and sold the same to a customer at 50% profit. The price at which he sold to the customer is

• A. 110
• B. 90
• C. 70
• D. 115
• E. 120

Answer 1

The Correct Option is D

To solve this problem, we need to calculate the selling price of the mixed nuts that a dry fruit seller prepared by mixing three kinds of nuts with different prices and sold at a 50% profit. We will follow these steps: 

1. Determine the cost price for each type of nut based on their given rates and the ratio in which they are mixed.
2. Calculate the total cost price of the mixed nuts.
3. Apply the profit percentage to find the selling price.

Step 1: Calculate the cost price for each type of nut.

• The costs per kg for the three kinds of nuts are 100/kg, 80/kg, and 60/kg, respectively.
• They are mixed in the ratio 3:4:5.
• Let the quantity of each type of nut be \(3x\), \(4x\), and \(5x\), respectively.
• Thus, the cost of nuts of the first type = \(3x \times 100 = 300x\).
• The cost of nuts of the second type = \(4x \times 80 = 320x\).
• The cost of nuts of the third type = \(5x \times 60 = 300x\).

Step 2: Calculate the total cost price.

The total cost of the mixed nuts = \(300x + 320x + 300x = 920x\).

Step 3: Calculate the selling price with 50% profit.

• Profit percentage is 50%.
• The formula for selling price (SP) = Cost Price (CP) + Profit.
• Profit = \(\frac{50}{100} \times \text{CP} = \frac{1}{2} \times 920x = 460x\).
• Therefore, SP = \(920x + 460x = 1380x\).

In terms of weight, since the original ratio was \(3 + 4 + 5 = 12\), the selling price per kg is:

SP per kg = \(\frac{1380x}{12x} = 115\)

Thus, the price at which the seller sold the mixed nuts to the customer is 115/kg.