Rule of Allegation

Introduction to Rule of Allegation

Using the rule of Alligation, two or more ingredients at a given price can be mixed to produce a mixture with the desired price if mixed in the correct ratio. Finding a weighted mean is all that is required to perform Alligation medial. Allegations can be made in two different ways.

Linking is the literal meaning of the word Allegation. Using lines or links to solve questions about a mixture gives the rule its name. The alignment method, not absolute values, percentage, ratio, rate, price, speed, etc., are all aligned. We can use Alligation whenever percentages, hours, kilograms, kilometres, etc., are compared.

Types of Allegation

• The rule of Allegation

It is a variation of the weighted average calculation. Assuming the ratio of two ingredients used if its Mean Price and the cost price per unit quantity of the mixture, is known.

Quantity of cheaper/ Quantity of dearer = (CP of Dearer – Mean Price) / (Mean Price – CP of cheaper)

• Repeated Dilution

Pure quantity remaining after ‘n’ processes of repeated replacement is calculated using this method. If ‘x’ units of a liquid are removed from a container and replaced by ‘y’ units of water, what happens? n operations later, a certain amount of pure

x*(1 – y/x)n

Rule of allegation tricks

• Additionally, allegations can be used in the context of partnerships, time and work, and wages to solve problems

• To resolve a problem, read a question and apply the aforementioned allegation rule to the values in the answer

• It may appear difficult to answer questions on this topic, but once a candidate has a basic understanding of the concept and important formulas, it is simple to solve

• It is not only possible to calculate the ratio between the quantities of two elements, but also the price at which an item can be sold

Rule of Alligation formula 

It is a variation of the weighted average calculation. Assuming a ratio of two ingredients is used and the Mean Price, the cost price per unit quantity of the mixture, is known.

Quantity of cheaper/ Quantity of dearer = CP of Dearer – Mean Price / Mean Price – CP of cheaper.

Rule of Allegation Derivation

Let’s say you go to the market and buy a certain amount of two different types of rice, each of which costs Rs. a per kg and Rs. B per kg, respectively. You can combine the two at home. Now, you’ll need to calculate the cost of the final product. The cost per kilogram of the mixture is the average or mean cost (m).

Due to this, it is obvious that the average cost will fall somewhere in between (a) and (b). Nonetheless, you’d prefer to know the average price. So, let’s try to figure out what it is.

Purchase x kilograms of the first type and y kilograms of the second. As a result, the total cost of your purchase is Rs. ax + by. In addition to the price, the total weight of the mixture is (x + y) kg. So mean average cost (m) =ax+by / x+y

This is nothing more than calculating the average weighted sum. Reformulating the equation:

ax+by / x+y

Or m(x + y)=ax + by

Or mx + my = ax + by

Or x (m-a) = y(b-m)

Or x / y=(b–m) / (m–a)

Hence, the rule of Allegation is said as :

Quantity of cheaper/ Quantity of dearer = CP of Dearer – Mean Price / Mean Price – CP of cheaper.

Rule of Allegation in Profit and Loss

Cost prices and profit/loss per cent on individual items are input into this formula to determine the overall profit or loss percentage.

For example, if we take,

Type A rice is sold for a 20 per cent profit, while type B rice is sold for a 15 per cent loss. To find the cost price of type A rice to type B rice, multiply the overall profit by 13.

By the rule of Allegation:

The ratio of the cost price of type A to type B rice = -28: -7

= 4: 1

The ‘–’ sign indicates a loss per cent.

A shopkeeper bought a table for Rs.1200 and sold it for 20 per cent profit; he bought a chair for Rs.400 and sold it for 10 per cent profit to find the overall profit percentage.

Let overall profit per cent = p%

By the rule of Allegation:

(10 – p): (p – 20) = 1200: 400 = 3: 1

10 – p = 3p – 60

4p = 70

P = 17.5

Hence, overall profit percent = p = 17.5%.

Conclusion

Problems with mixtures of ingredients can be solved using the age-old technique of “allegation.” A mixture’s volume can be calculated using either an allegation medial or an allegation alternate, both of which can be used to calculate the amount of each ingredient required to create a specific volume of the final mixture. Finding a weighted mean is all that is required to perform Allegation medial. Alternate ligation involves organizing the ingredients into high and low pairs, which are then traded off and are more complicated.