**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

### 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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