One quality of Rice costs Rs.45/Kg is mixed with another quality of rice at a certain rate in the ratio of 3:2. If the mixture so formed is worth Rs.50/Kg, What is the rate per Kg of the second quality of rice?
Question
One quality of Rice costs Rs.45/Kg is mixed with another quality of rice at a certain rate in the ratio of 3:2. If the mixture so formed is worth Rs.50/Kg, What is the rate per Kg of the second quality of rice?
Solution
To solve this problem, we can use the concept of weighted averages.
Step 1: Identify the given values. The cost of the first quality of rice is Rs.45/Kg. The cost of the mixture is Rs.50/Kg. The ratio in which the two qualities of rice are mixed is 3:2.
Step 2: Let's denote the cost of the second quality of rice as 'x'.
Step 3: Set up the equation based on the concept of weighted averages. The weighted average price of the mixture is given by the sum of the products of the quantities and their respective prices, divided by the total quantity.
So, (345 + 2x) / (3 + 2) = 50
Step 4: Simplify the equation. 135 + 2x = 250
Step 5: Solve for 'x'. 2x = 250 - 135 2x = 115 x = 115 / 2 x = Rs.57.5
So, the rate per Kg of the second quality of rice is Rs.57.5.
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