If a person mixes two types of tea costing $20 and $30 per kg in the ratio 2:3,

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Question: If a person mixes two types of tea costing $20 and $30 per kg in the ratio 2:3, what is the cost price per kg of the mixture?

Options:

Correct Answer: $26

Solution:

Cost = (2*20 + 3*30) / (2 + 3) = (40 + 90) / 5 = 130 / 5 = $26.

If a person mixes two types of tea costing $20 and $30 per kg in the ratio 2:3, what is the cost price per kg of the mixture?

If a person mixes two types of tea costing $20 and $30 per kg in the ratio 2:3, what is the cost price per kg of the mixture?

Step 1: Identify the cost of the first type of tea, which is $20 per kg.
Step 2: Identify the cost of the second type of tea, which is $30 per kg.
Step 3: Determine the ratio in which the two types of tea are mixed, which is 2:3.
Step 4: Calculate the total cost contributed by the first type of tea: 2 kg * $20/kg = $40.
Step 5: Calculate the total cost contributed by the second type of tea: 3 kg * $30/kg = $90.
Step 6: Add the total costs from both types of tea: $40 + $90 = $130.
Step 7: Calculate the total weight of the mixture: 2 kg + 3 kg = 5 kg.
Step 8: Find the cost price per kg of the mixture by dividing the total cost by the total weight: $130 / 5 kg = $26.

Weighted Average Cost – The question tests the ability to calculate the average cost of a mixture based on the ratio of the components and their individual costs.
Ratio and Proportion – Understanding how to apply ratios to determine the contribution of each component in a mixture.