Two varieties of tomatoes are bought in the ratio 2 : 3, where the price of first variety is twice that of the second. The varieties are mixed and sold at Rs. 17.50 per kg, resulting in a profit of 25%. Find the costs of the two varieties before selling.

The two varieties of tomatoes are bought in the ratio 2 : 3

The price of the first variety is twice the price of the second variety.

The mixture is sold at Rs. 17.50 per kg, resulting in a profit of 25%.

The cost price (CP) of the mixture can be determined using the selling price (SP) and the profit percentage:

CP of mixture = $$\frac{\text{SP of mixture}}{1 + \frac{\text{Profit Percentage}}{100}}$$​​

Let the CP of the second variety be x. Then the CP of the first variety is 2x.

​$$\text{CP of mixture} = \frac{\text{SP of mixture}}{1.25}$$​​

​$$\text{CP of mixture} = \frac{17.50}{1.25} = 14 \, \text{Rs/kg}$$​​

Using the weighted average formula:

​$$\text{CP of mixture} = \frac{2 \cdot \text{CP of first variety} + 3 \cdot \text{CP of second variety}}{2 + 3} \\ \ \\14 = \frac{2(2x) + 3(x)}{5} \\ \ \\14 = \frac{4x + 3x}{5}\\ \ \\14 = \frac{7x}{5}\\ \ \\7x = 14 \times 5 = 70 \\ \ \\x = 10 \, \text{Rs/kg}$$​​

Thus,

The CP of the second variety is x = 10 Rs/kg
The CP of the first variety is 2x = 20 Rs/kg

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