PROBLEMS ON AVERAGE - 1

Examples 1: what will be the average of 11, 12, 13, 14, 15, 16, 17 series?

Solution: The common difference is same i.e., 1, so the series is in A.P. Average is the middle term when the number of terms is odd, So the middle term is 14 which is our average of the series.

Example 2: What will be the average of 11, 12, 13, 14, 15, 16, 17, 18?

Solution: Since the common difference is same for each of the term we can say that the series is in A.P. So we have discussed that when the number of terms are even then the average will be the average of two middle terms.

Now the two middle terms are 14 and 15, and the average is (14+15)/2 = 14.5

Example 3: The average of five numbers is 29. If one number is excluded the average becomes 27. What is the excluded number ?

Solution: let the excluded number is

= (29 x 5) – ( 27 x 4 )

= 145 – 108

= 37 .

Example 4: Find the average of first 20 natural numbers?

Solution: 

Sum of first n natural numbers = n ( n + 1 ) /2

So, we can find easily average of first 20 natural numbers 20 x 21 / 2 = 210 

So, then Required average is = 210 / 20 = 10.5.

Example 5 : Find the average of first 20 multiplies of 5 .

Solution: 

Required average = 5 ( 1 + 2 + 3 +……………….. + 20) /20

= ( 5 x 20 x 21 / 20 x 2) = 2100 / 40 = 52.5 .

So the Required average is 52.5.

Average || Important Formulas and Shortcuts of Average

          Dear readers, we all know that speed and accuracy in calculation is much needed for Quantitative Aptitude section of various competitive exams and if we know enough Short Tricks in Quantitative Section, we will surely score better in the section. So, let us make it easy for all of you through these Simple and Easy tricks on Average which will not only make quantitative questions easy but  also save our time. The tricks will be helpful for the upcoming Indian RRB Exam , SSC CGL Exam and much more.

What is Average?

          Average is obtained by adding several quantities together and then dividing this total by the number of quantities given. 

The main term of average is equal distribution of a value among all which may distribute persons or things.

Here is average based some fact and formula and some average shortcut tricks examples.

Formula:

· Average = (Sum of observations / Number of observations).

Find the Average Speed

· Average Speed = (Total Distance Covered/Total Time Taken).

· If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by-   

· If a person covers A km’s at x km/hr and B km’s at y km/hr and C km’s at z km/hr, then the average speed in covering the whole distance is- 

· If value of each term increases/decreases by ‘x’, then the average of the group also increases/decreases by ‘x’.

· There are two batches A and B in a class. If we have to find the average of the whole class use the formula:
Batch A: Number of students = a
                  Average of batch A = x
Batch B: Number of Students = b
                  Average of batch B = y

Average of whole class (Batch 1 and Batch 2) = (ax + by)/(a + b)

When a person leaves the group and another person joins the group in place of that person then-

· If the average age is increased,
Age of new person = Age of separated person + (Increase in average × total number of persons)

· If the average age is decreased,
Age of new person = Age of separated person – (Decrease in average × total number of persons)

When a person joins the group 

In case of increase in average age

· Age of new member = Previous average + (Increase in average × Number of members including new member)

In case of decrease in average age

· Age of new member = Previous average – (Decrease in average × Number of members including new member)

If the numbers are in Arithmetic Progression there are two cases

· when the number of terms is odd the average will be the middle term.

· when the number of terms is even then the average will be the average of two middle terms.

PROBLEMS ON AVERAGE - 1