Question

11. Two ingredients costing *c per unit and * d per unit (c < d) are mixed together to obtain a
mixture at m per unit, then
Quantity of cheaper ingredient
Quantity of dearer ingredient

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Answer 1

☆ Answer

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 xx units of a liquid from which yy units are taken out and replaced by water. After nn operations, quantity of pure liquid

=x(1−yx)n=x(1−yx)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)