TRICKS TIPS AND SHORTCUTS FOR SOLVING PROBLEMS IN MIXTURE AND ALLIGATION

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INTRODUCTION TO MIXTURE AND ALLIGATION:

Hi Aspirants today we are going to discuss on a topic Mixture and Alligation. This  topic carries 1 mark in prelims and 2 mark in mains exam.This topic can be implemented in Topics such as Time and Distance ,Ratio and Proportions.

MIXTURE:

When two or more components are mixed together then it is known as Mixture

Mixture is of two types they are:

1.Simple Mixture:When two or more different ingredients are mixed together,a simple mixture is formed

2.Compound Mixture:When two or more simple mixtures are mixed together, a compound mixture is formed.

ALLIGATION:

It 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.

Where M=Mean Value which is between X and Y, X=Cheaper Price, Y=Price higher than the Mean Value

#.1.TYPE 1:

MIXTURE CONTAINING TWO OR MORE INGREDIENTS:

1.A shopkeeper sells rice of 1kg for Rs.75 w two quality of rice whose worth for 1kg is Rs.70 and Rs.80.

Therefore for 1kg of rice the two quality of rice should be mixed in the ratio  1:1

 TYPE  2:

BASED ON PROFIT OR LOSS:

1.A dishonest  milkman professes to sell his  milk at cost price but he mixes it with water and thereby gains 25%.The percentage of water in the mixture?

Let the Cost Price of  Pure Milk be Rs.1,

Selling Price of (Milk+ Water) is also Rs.1. which is 25% more than the Costprice

Therefore CostPrice = (100/125)*1=(4/5)

The Percentage   of water mixed in the mixture =*100=20%

2.The Ratio ,in which tea costing Rs.192 per kg is to be mixed  with tea  costing Rs.150 per kg so that the mixed tea  when  sold for Rs.194.40 per Kg,gives a profit of 20%.

Finding   Selling Price after Giving Profit over Cost Price:

Let the Cost Price be X

Selling Price=X*(120/100)  = 194.40

X=(19440/120) ⇒ X=162

30:12   ⇒        5:2

The 1^st and 2^nd quality of rice should be mixed in the ratio:5:2

Remember:

If there is a loss in the transaction indicate it by the ‘-‘ negative sign before the number.