In what ratio must rice costing ₹ 40 per kg be mixed with rice costing ₹ 55 per kg so that the mixture costs ₹ 45 per kg?
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B — 2 : 1
Detailed Solution
Alligation: cheaper : dearer = (55 − 45) : (45 − 40) = 10 : 5.
10 : 5 = 2 : 1.
✓ Check
2 kg at 40 and 1 kg at 55 cost 135 for 3 kg, i.e. ₹ 45 per kg.⚠ Common trap
(A) 1 : 2 — writes the differences against the wrong prices.Quick tip
Cheaper : dearer = (dearer - mean) : (mean - cheaper)
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Ask a doubtMore Alligations Questions
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- Q4.Gold is times as heavy as water and copper is times as heavy as water. In what ratio should these be mixed to get an alloy times as heavy as water?
- Q5.Two liquids A and B are in the ratio 5 : 1 in container 1 and in the ratio 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?
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Alligations — Preparation
This question tests your understanding of Alligations, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Alligation is a quick method for finding the ratio in which two ingredients at different prices or concentrations must be mixed to get a mixture at a given mean price or concentration. The rule of alligation is: (cheaper quantity) : (dearer quantity) = (dearer price - mean price) : (mean price - cheaper price). Exam questions involve mixing two varieties of rice, tea or other goods, milk and water mixtures, solutions of different concentrations, and replacement problems, where part of a mixture is removed and replaced with water again and again. For repeated replacement, the quantity of the original liquid left is x(1 - y/x)^n, where x is the total quantity, y is the amount removed each time and n is the number of operations. Alligation also works for averages, speeds and profit percentages, which makes it a powerful shortcut across many topics. Practise the alligation and mixture questions below, each with a step-by-step solution.