Arithmetic question accounts for a good number of questions in Elementary mathematics section. Mixture and Alligation is the topic which is asked in almost all the law entrance exam. We are sharing today Important Short tricks on Mixture and alligation topic. These short tricks will help you all in solving the question in minimum time. So let's study Basic Concept and Tricks on Mixture and alligation which will be very helpful for upcoming Law entrance Exam.

Alligation 

(i) To find the mean or average value of mixture: When the prices of two or more ingredients which may be mixed together and the proportion in which they mixed are given (this is alligation Method); and

(ii) To find the proportion in which the ingredients at given prices must be mixed to produce a mixture at a given price. This is alligation Alternate.

Note:

(1) The word alligation literally means linking. The rule takes its name from the lines or links used in working out questions on mixture.

(2)Alligation method is applied to a percentage value, ratio, rate, prices, speed etc and it is not applicable for absolute values. It means whenever percent, per hour, per kg, per km etc, are being compared, we can use alligation.

Rules of Alligation

if the gradients are mixed in a ratio, then

We represent it as under:

Then, (cheaper quantity) : (dearer quantity) = (d – m ) : (m – c)

Solved problems:

Ex1:  In what proportion must rice at Rs3.10 per kg be mixed with rice at Rs3.60 per kg, so that the mixture be worth Rs3.25 a kg?

Solution:

By the alligation rule :

they must be mixed in the ratio 7 :3.

Milk and Water

Ex2: A mixture of a certain quantity of milk with 16 liters of water is worth 90 P per liter. If pure milk is worth Rs1.08 per liter, how much milk is there in the mixture?

Solution:

.

By the alligation Rule, milk and water are in the ratio of 5: 1.

quantity of milk in the mixture = 5 ×16 = 80 litres.

Ex3: 300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% of the solution?

Solution:

The existing solution has 40% sugar, and sugar is to be mixed; so the other solution has 100% sugar. So, by alligation method;

the two mixture should be added in the ratio 5: 1

Therefore, required sugar =(300/5)*1 = 60

Direct formula :

Quantity of sugar added = 

In this case,

Ans = 300(50-40)/100-50 

=  600 gms

Question: The container contains 75 liters of pure honey. 2/5th of the pure honey is replaced by milk in the container. Again two-fifth of the mixture is extracted and an equal amount of milk is added. What is the ratio of honey to milk in the new mixture?

Answer: Total quantity of pure honey in container = 75 liters 
Quantity of pure honey in container = 75 liters 
2/5th of the pure honey is replaced by milk in the container. Again two-fifth of the mixture is extracted and an equal amount of milk is added. 
⇒ The operation took place 2 times and amount replaced each time is 2/5 
∴Amount of honey left after 2 operations = 75(1-2/5)²
⇒ Amount of honey left after 2 operations = 75(3/5)² 
⇒ Amount of honey left after 2 operations = 75 × 9/25 
⇒ Amount of honey left after 2 operations = 27 liters 
Now, required ratio =  
Hence, the ratio of honey to milk in the new mixture is 9: 16