A wholesaler decides to mix two varieties of lentils worth Rs. 170 per kg and Rs. 180 per kg with a third variety of lentils in the ratio 1:2:3. What is the price per kg of the third variety of lentils if the lentil mixture is worth Rs. 173 per kg?

A. Rs. 174.30
B. Rs. 178.33
C. Rs. 176.40
D. Rs. 169.33

The price per kg of the third variety of lentils is Rs. 169.33. This is determined using the given price of the lentil mixture, the prices of the first two types of lentils, and the ratio in which these lentils are mixed.

Explanation:

The subject of your question is on the mathematics topic of ratios and averages. Given the information, we need to find the price per kilogram of the third variety of lentils. In the ratio 1:2:3, the first, second, and third types of lentils have quantities of 1 part, 2 parts, and 3 parts, respectively, making the total parts 6.

Next, we calculate the total price for all parts. Given that the mixture is worth Rs. 173 per kg, an average price based on the ratios, we multiply this by the total parts (6), which equals Rs. 1,038.

We also calculate the total cost of the first two varieties of lentils. The first is Rs. 170 per kg, contributing 1 part out of the total 6, so its total cost is 170 x 1 = 170. The second is Rs. 180, and it contributes 2 parts, so its total cost is Rs. 360.

Given that, the cost of the third type of lentils is then found by subtracting the total cost of the first two types of lentils from the total for the mixture, so Rs. 1038 - Rs. 530 (Rs. 170 + Rs. 360) = Rs. 508. The price per kg of the third type of lentils is Rs. 508 / 3 (since it contributes 3 parts in the ratio 1:2:3) = Rs. 169.33 per kg.

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