Alligation or Mixtures

1) Rule of alligation:

Points to Remember While Using the Rule of Alligation

• The three values alligated should always represent the same variable and should have same units.
• alligation of 3 values of cost gives the ratio in terms of number and vice-versa.
• If two values of cost price and selling price of the mixture are given, then in such cases first calculate the cost price of the mixture and then allegate the 3 values of cost price.
• A and B represent concentration if the numerical is based on mixing of solutions.

Applications Of Mixtures

Consider the following common data to understand the application better. A= 20 B=10 Na =30 Nb= 45 The answer will be 14, in each of the following cases.

Average of a class

Example

Class A has 30 students scoring average marks of 20 and Class B has 45 students scoring average marks of 10.What is the average of both classes together (14).

Average price of goods

Example

Sunita buys 30 kgs of sugar at Rs 20/kg and 45 kgs of sugar at 10/kg. What is the average price? (Rs 14/kg).

Percentage

Example

An antique article salesman makes a profit of 20% by selling 30% of his articles and a profit of 10% by selling 45% of his goods.

What is his net percentage profit? (14%).

Average Speed

Example

A bus travels at 20kmph for 30 km and at 10 kmph for 45 km.

Find the average speed of the bus for the entire journey (14kmph).

Mixtures

Example

A dishonest milkman dilutes two milk cans such that milk can A containing 30 liters is mixed with 20% water and milk can B containing 45 liters is mixed with 10% water. He combines both mixtures. Find the percentage of water in the final mixture (14%).