Alligations Questions with Solutions
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.
- Q1.
The ratio of alcohol to water in two containers A and B is 5 : 3 and 1 : 3 respectively, with both containers having infinite capacity. The aim is to obtain 2.1 litres of liquid composed of equal quantities of alcohol and water. How much liquid should be drawn from A (in litres)?
A. 1.4B. 1.05C. 0.35D. 1.1mediumAsked in NIMCET 2026View solution › - Q2.
A vessel contains 95 litres of a mixture of milk and water in the ratio 15 : 4. P litres of the mixture are taken out and 18 litres of water are added to the rest. The new ratio of milk to water becomes 3 : 2. Find the value of P.
A. 57B. 38C. 27.5D. 19mediumAsked in NIMCET 2023View solution › - Q3.
A 30-litre mixture of milk and water contains 10% water. How much milk should be added so that the percentage of water in the mixture comes down to 2%?
A. 60 litresB. 90 litresC. 80 litresD. 120 litreseasyAsked in NIMCET 2023View solution › - 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?
A. B. C. D.easyAsked in NIMCET 2008View solution › - Q5.
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?
A. 1 : 2B. 2 : 1C. 3 : 2D. 5 : 10easyView solution › - Q6.
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?
A. 2 : 3B. 4 : 3C. 3 : 2D. 3 : 4mediumAsked in NIMCET 2019View solution ›