In what ratio should tea costing ₹62 per kg be mixed with tea costing ₹72 per…
2023
In what ratio should tea costing ₹62 per kg be mixed with tea costing ₹72 per kg so that the mixture costs ₹64.50 per kg?
Answer: A. 3 : 1 — ConceptWhen two ingredients with different unit prices are mixed to obtain an intermediate price, the alligation rule compares each ingredient's distance from…
- A.
3 : 1
- B.
3 : 2
- C.
4 : 3
- D.
5 : 3
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Show answer & explanation
Correct answer: A
Concept
When two ingredients with different unit prices are mixed to obtain an intermediate price, the alligation rule compares each ingredient's distance from the mean price.
The quantity ratio of the cheaper ingredient to the dearer ingredient is (dearer price − mean price) : (mean price − cheaper price).
Application
Let the required quantities of the ₹62 tea and the ₹72 tea be x kg and y kg respectively.
By the weighted-average equation, 62x + 72y = 64.50(x + y).
Rearranging gives 64.50x − 62x = 72y − 64.50y, so 2.50x = 7.50y.
Therefore x : y = 7.50 : 2.50 = 3 : 1.
Cross-check
Using three equal parts of ₹62 tea and one equal part of ₹72 tea gives (3 × 62 + 1 × 72) ÷ 4 = 258 ÷ 4 = ₹64.50 per kg.
Hence, the tea costing ₹62 per kg and the tea costing ₹72 per kg should be mixed in the ratio 3 : 1.