Difficulty: Easy
Correct Answer: 1 : 3
Explanation:
Introduction:
This question tests the alligation (weighted average) concept used in mixtures. When two items with different costs are mixed, the mean price of the mixture depends on how much of each item is used. Alligation gives a quick way to find the required mixing ratio without solving lengthy equations. Here, we are mixing two teas costing Rs 300/kg and Rs 200/kg to obtain a mixture costing Rs 225/kg. We must find the ratio in which the Rs 300/kg tea and the Rs 200/kg tea are combined.
Given Data / Assumptions:
Concept / Approach:
By alligation, the required quantities are in the inverse ratio of the differences from the mean: quantity of dearer : quantity of cheaper = (mean - cheaper) : (dearer - mean). This works because the extra cost paid for the dearer item must be balanced by the savings from the cheaper item to land exactly at the mean cost.
Step-by-Step Solution:
Step 1: Compute differences from the mean cost.mean - cheaper = 225 - 200 = 25dearer - mean = 300 - 225 = 75Step 2: Apply alligation ratio.Quantity of Rs 300 tea : Quantity of Rs 200 tea = 25 : 75Step 3: Simplify the ratio by dividing by 25.25 : 75 = 1 : 3
Verification / Alternative check:
If we take 1 kg of Rs 300 tea and 3 kg of Rs 200 tea, total cost = 1*300 + 3*200 = 300 + 600 = 900. Total quantity = 4 kg. Average cost = 900/4 = 225 per kg, which matches the required mean. So the ratio is correct.
Why Other Options Are Wrong:
3 : 1 gives a mean much closer to Rs 300, so it exceeds Rs 225.2 : 5 and 5 : 2 produce different weighted averages, not Rs 225.4 : 1 is also too heavy on the Rs 300 tea, so the mean becomes higher than Rs 225.
Common Pitfalls:
• Reversing the ratio (writing 3 : 1 instead of 1 : 3).• Subtracting in the wrong order while computing differences.• Forgetting that quantities are inversely proportional to the price differences from the mean.
Final Answer:
Tea costing Rs 300/kg should be mixed with tea costing Rs 200/kg in the ratio 1 : 3.
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