Aptitude Questions and Answers

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 a desired price.

*A process or rule for the solution of problems concerning the compounding or mixing of ingredients differing in price or quality.*

*Merrian - Webster Medical Dictionary*

The cost price of a unit quantity of the mixture is called the mean price.

If two ingredients A and B of price x and y respectively are mixed and the price of resultant mixture is M (mean price)then the ratio (R) in which ingredients are mixed is given by, **the rule of allegation**

$$ R = \left(\dfrac{M-y}{x-M}\right)$$

The above formula can be represented in diagram below, which in turn is more intuitive to grasp

Ingredient A Ingredient B

(Price x) (Price y)

\ /

Mean

(Price M)

/ \

(M – y) : (x – M)

Thus the required ratio is,

$$ R = \left(\dfrac{M-y}{x-M}\right) = \left(\dfrac{y - M}{M - x}\right)$$

Suppose a container contains a solution from which some quantity of solution is taken out and replaced with one of the ingredients. This process is repeated n times then,

$\text{Final Amount of ingredient that is not replaced}=$

$$\text{Initial Amount} \times \left(\dfrac{\text{Vol. after removal}}{\text{Vol. after replacing}}\right)^n$$

Above formula is not only true for absolute amounts but for ratios as well. So following formula is also valid:

$\text{Final ratio of ingredient not replaced to total}=$

$$\text{Initial ratio} * \left(\dfrac{\text{Vol. after removal}}{\text{Vol. after replacing}}\right)^n$$