Mixture and Alligation: Formula and Tricks with Problem (Question) and Solutions

Important Rule

A container initially contains ” x ” units of a liquid. If ” a ” unit of liquid is taken out and it is filled with ” a ” unit of water repeatedly upto n times, then the final quantity of the original liquid in the container is given as

Mixture

The new product obtained by mixing two or more ingredients in a certain ratio is called mixture.

Mean Price

The cost price of a unit quantity in the mixture is called the mean price. It will always be higher than cost price of cheaper quantity and lower than the cost price of dearer quantity.

Rule of alligation

It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price. Let the cost price of a unit of cheaper article is c and that of a unit of costly article is d and the average (mean) price of mixture is m, then

Quantity of cheaper article Quantity of costly article Cost price of a unit costly article - Mean price Mean price- Cost price of a unit of a cheaper article

Examples

Ex: In a mixture of 60 L, the ratio of ethanol to ether is 4:1. The quantity of ether to be added to the mixture to make this ratio 2:1 will be

(a) 10 L

(b) 12 L

(c) 14 L

(d) 16 L

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