Preparing for DRDO CEPTAM Tier I - Average

As promised we are back with tricks and tips to help you prepare Tier-1. In the next few posts we will cover various topics of Quantitative Aptitude Test.

Lets start with "AVERAGE". Below is the formula to calculate Average:

Average = Sum of Observations ÷ Number of Observations

Lets solve some questions now based on above formula.

Example 01: Pawan scored 78, 74, 70 & 80 marks in Math, Science, Computers and English respectively? What is his average marks.

Solution: 

      Average = Sum of Observations ÷ Number of Observations
      Average = (78 + 74 + 70 + 80) ÷ 4
                  = (302) ÷ 4 = 75.5

So, Pawan's average marks is 75.5

Lets solve another example.

Example 02: What is the average of first three even numbers starting from 20?

Solution: First three even numbers are : 20, 22, 24.
If we apply the above formula, average will be:
                 (20 + 22 +24) ÷ 3 = 66.

Average is also used in groups. Here are few tips.

When a person is replaced by another person in a group

If average is increased then:

Age of new person = Age of person left + (Increase in average  x total number of persons)

If average is decreased then:

Age of new person = Age of person left - (Decrease in average  x total number of persons)

When a person joins the group

If average is increased then:

Age of new person = Previous Average + (Increase in average x total members including new member)

If average is decreased then:

Age of new person = Previous Average - (Decrease in average x total members including new member)

Lets apply the above shortcuts in few examples.


Example 03: Average age of class-X is 15 years. If class teacher age is included, average is increased to 16 years. Total students in class is 30. What is the age of teacher?

Solution: Lets apply one of the above formula.

Age of new person = Previous Average + (Increase in average x total members including new member)

So, Age of teacher = 15 + ( 1 x 31) = 15 + 31 = 46.

Solve this question with another method:
 Students Age = 30 x 15 = 450
 Combined Age of Students and teacher = 31 x 16 = 496.

Teacher's age = Combined Age - Students'age
                     = 496 - 450
                     = 46 Years.


Next, we will learn how to calculate average speed.

Suppose Pawan covers a distance @ x km/hr and same distance @ y km/hr then average speed to cover whole distance is :

Example 03: While going to office Pawan drives his car @ 40 km/hr, and while coming back from office, he cover save distance @ 35 km/hr due to traffic. What is Pawan's average speed?

Solution: Lets apply the above formula and solve it.

So the average speed is 37.33 km

Suppose a person covers x km @ a km/hr, y km @ b km/hr and z km @ c km/hr, then average speed to complete whole distance is :

Hope you find these tips helpful. For now practice with above formula. Tomorrow we will post a quiz on Average to brush up what we learnt today.

If you are looking for few book recommendation here three books I recommend:

Cheapest one is this.

You can also consider below two:

S.Chand Quantitative Aptitude
McGraw Hill 


Keep Practicing.