Important Concepts and Formulas – Mixture and Alligation1. Alligation

Alligation is the rule which enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a specified price.

2. Mean Price

Mean price is the cost price of a unit quantity of the mixture

3. Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations, quantity of pure liquid =x(1−y/x)^{n}units.

4. Rule of Alligation

If two ingredients are mixed, then (Quantity of cheaperQuantity of dearer)(Quantity of cheaperQuantity of dearer)=(CP of dearer – Mean PriceMean price – CP of cheaper)=(CP of dearer – Mean PriceMean price – CP of cheaper)

The above formula can be represented with the help of the following diagram which is easier to understand.

=> (Cheaper quantity) : (Dearer quantity) = (d – m) : (m – c)

A container contains 50 litres of milk. From this container, 10 litres of milk was taken out and replaced by water. This process is repeated one more time. How much milk is now left in the container?

In what ratio must a shopkeeper mix two types of rice worth Rs. 50 kg and Rs. 70 kg, so that the average cost of the mixture is Rs. 65 kg?

In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.