Quantitative Aptitude Notes

# Averages Mixtures Alligations

### AVERAGES MIXTURES ALLIGATIONS

Hello Uotians, Averages Mixtures Alligations is a very interesting topic from the Quant section of MBA Entrance Exams as well as Bank Exams.

#### Concept

Averages Concept

Average or Mean is nothing but the sum of all the entities given divided with the number of entities

Example: The average of numbers 5, 9 and 16  is

(5+9+16)/3 = 30/3 = 10

Mixture Alligation Concept

When we mix 2 or more entities, a mixture is obtained. Alligation is linking when different mixtures are added and other parameters like cost, profit etc. comes into the picture.

Alligation Rule #### Solved Examples

Averages

In Ashish’s opinion, his weight is greater than 55 kg but less than 62 kg. His father does not agree with Ashish and he thinks that Ashish’s weight is greater than 50 kg but less than 60 kg. His sister’s view is that his weight can’t be greater than 58 kg. If all of them are correct in their estimation, what is the average of different probable weights of Ashish?

Let Ashish weight X kg.
According to Ashish , 55 < X < 62
According to Ashish’s father, 50 < X < 60
According to Ashish’s sister, X < 58
The values satisfying all the above conditions are 56 & 57.
Therefore, Required average = (56 + 57)/2 = 113/2

So, Ashish’s weight is 56.5 kg.

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

Mixtures & Alligations

In 4 litres of milk and water mixture, the concentration of milk is 80%. A woman takes out 20% of the total mixture and adds the same quantity of water. With the total quantity of the new mixture, she wants to prepare coffee where the concentration of water should be 60%. How many litres of more water will she require to prepare coffee?

Solution:

In 4 litres mixture, the quantity of water = 20% of 4 = 0.8 litres and the quantity of milk = 80% of 4 = 3.2 litres
In 20% of the mixture i.e. 20% of 4 = 0.8 litres, the quantity of milk = 80% of 0.8 = 0.64 litres

The quantity of water = 20% of 0.8 = 0.16 litres
She adds the same quantity of water, In the new mixture, the quantity of milk = (3.2 – 0.64) = 2.56 litres

The quantity of water = (0.8 – 0.16 + 0.8) = 1.44 litres
Total quantity of mixture = 4 litres

Let say she require x litres of water then 40% of (4 + x) = 2.56
1.6 + 0.4x = 2.56
0.4x = 2.56 – 1.6 = 0.96
x = 2.4 litres

Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?