# How to Solve Questions on Average without the Average Formula

### In this post we will discuss how to solve questions on average without using the formula, that will help you to save time in Bank and SSC Exams.

Quantitative Aptitude is an integral part of all Bank and SSC Exams. Questions on Average are asked in most competitive exams and using the Average formula to solve them is not a very good idea when you want to save time.
The only difference between candidates who get selected and candidates who don’t get selected is time management which is because of the use of smart methods to solve problems. So this is a series of blog posts about smart methods that will help you solve questions in 5- 10 seconds that would otherwise take much longer.

### What is Average?

Average is a standard mathematical operation that usually involves finding the central value from amongst a group of values. It is also described as equal distribution of the given amount among the group. Defined in mathematical terms it is the numerical result obtained by dividing sum of two or more quantities by the number of quantities.
One of the most popular models of questions asked in averages is when a value is replaced, removed or added from the group and its impact in the group average.

## What is the Average Formula?

We have all been using this formula to solve questions on averages since our school days and know it by heart! Interestingly, this formula can be used to solve all kind of questions for averages.

### Example of a Question on Average

The average age of 39 students and a teacher of a Class are 11 years. If the age of the teacher is excluded the average age of class is reduced by 1. What is the age of the teacher?

1) 49 years      2) 39 years      3) 50 years      4) 52 years      5) None of these

### Conventional Method - Using the Average Formula

So how do you always solve this question? Scribble down some numbers on a sheet of paper and start multiplying, adding, subtracting and dividing.
Step 1:
The average of 39 students + 1 teacher = 11
Step 2:
Sum of ages of 39 students + 1 teacher= 11x (39+1)= 440 (i)
Step 3:
When the teacher is excluded from for the average age the new average= 11- 1= 10
Step 4:
The sum of the ages of 39 students= 39x 10= 390 (ii)
Step 5:
Teacher’s age= (i)- (ii)= 440- 390= 50
Phew that was 45 valuable seconds of a competitive exam! That’s just too much calculation for a simple problem like this which can actually be solved in just one line.

### Smart Method without the Average Formula

Now get ready for a smart solution that will help you save at least 30 extremely precious seconds! After all time saved in an exam is actually the extra time that you earn for yourself.
When the teacher leaves the group, he/ she takes with him/ her 1 year (the change in the new average) from each of the 39 students along with the 11 years of his/her average age.
Step 1:
(39 x 1)+ 11= 50
This implies that if a value leaves the group, the value takes with it the change multiplied by the number of values and of course the old average, since it was also a part of the group.

Isn’t this just awesome! Hardly 10 seconds and an answer to a question that originally required so much calculation!

Watch this amazing short cut.

Practice Questions on Average
Why don’t you try to solve these questions by using the smart method and not the average formula!

The average age of 50 students and a teacher of a Class are 12 years. If the age of teacher is excluded the average age of class is reduced by 1. What is the age of teacher?
a)62 years      b) 60 years      c) 61 years      d) 53 years      e) None of these

The average age of 30 students is 9 years. If the age of their teacher is included, it becomes 10 years. The age of the teacher is
a) 28 years      b) 30 years      c) 40 years      d) 43 years      e) None of these