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Average:

Concept of Average problem

Nowadays from the arithmetic part, a lot of questions are asked in the banking exam. 

Average is an important topic in the arithmetic section. It will be helpful in another section also.

Concept of Average:

The concept of average is equal distribution of the overall value among all things.

Some important formula related to Average:

Example 1:

Let us take an example, 

Find the average of 10, 12,15,17,26.

Solution: 

Now, whenever smaller values are given this formula is easy.

But when we have to find these type of values like = 58, 76, 84, 94, 98

Then this formula will be time consuming. So we need to find a shortcut.

At first, we need to find the highest and the lowest number. Average always lies between highest and lowest number.

For this example, the highest number is 98

The lowest number is 58

We need to choose any number between the highest and lowest number.

Suppose we choose 75. You can choose any other number.

Now, we need to calculate the deviation of all numbers from 75.

So, now we need to calculate the net deviation from the supposed value.

Net deviation from the supposed value   

So, the actual average is (supposed value + net deviation) = 75 + 7 = 82

So, in this way, we can calculate the average of many numbers easily.

Few types of questions come in exams based on the theory of average.

Problems related to age:

Before discussing the question we need to understand that 

If the present age of a person is M years

Then after N years, his/her age will be (M+N) years

Before N years his/her age was (M-N) years

(Q1): In a family, there are 8 members whose current average age is 25years. In this family, a child was born 4 years ago. Then what is the average of the family at the time of birth of that child?

Solution:
 Let the average of 7 members excluding the child is x years at the time of the birth of that child.

So, the average age of the family was 28 years at the time of the child’s birth.

Problems related to replacement:

(Q1): The average age of 12 person is decreased by 3 years when one of them having 50years is replaced by a new person. Then what is the weight of the new person?

Solution:

So, we can calculate it by using the traditional method but that will be very time consuming.

So, we will solve it in this way.

In this question, it is said that the average of 12 persons is decreased by 3.

So, the total age of 12 persons is decreased is (12 * 3) = 36 years.

This 36 years of age is decreased due to the replacement of a person having age 50 years by a new person.

So, the weight of the new person is (50 - 36) years = 14years.

Note:  We can also calculate the age of a new person if the average age is increased.

(Q2): There are 20 members in a group. Whose average age is 25 years. If one member joins the group then the average age of that group is increases by 1 year. Then what is the age of the new member?

Solution: 

Now, after joining the new person that total group member is (20 + 1) = 21 years.

The average is increased by 1 year.

So, the total age increased of that group is (21 * 1) = 21 years.

Now this age is increased for the new member

So, the age of the new member is (25 + 21) years = 46 years.

We can also solve this problem by the traditional method. But it will be time consuming. 

The average age of 20 members was 25 years.

The total age of 20 members was (25 * 20) years = 500 years

In this case average of the group increases by 1 year, so it means that the age of the person who joins the group must be greater than the average.

Now after joining one member the average age increases by 1 year.

So, the new average of 21members is 26 years.

So, the total age of 21 members is (26 * 21) years = 546 years.

So, the age of the new member is (546 - 500) years = 46 years.

This process is very much calculative. So, try to solve using the first process.

Now, if in the above question the average age is decreased or a member left a group then we can calculate the age of the person by this method.

For other types of problems please visit the next chapter: Different type of problem of Average