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# Quant Booster on Average for Teaching Exams

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Table of content

Dear readers, you all know that speed in calculation sets the complete base for **Quantitative Aptitude section** of various competitive exams and if you know enough **Short Tricks in Quant Section**, you 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 quant questions easy but will also save your time. The tricks will be helpful for the upcoming teaching **2017 Exam**.

**Important Formulas and Shortcuts of Average**

**What is Average?**

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

The main term of average is the **equal distribution of value** among all which may distribute persons or things. We obtain the average of a number using a formula that is the sum of observations divided by Number of observations.

Here are an average based some fact and formula and some average shortcut tricks examples. The problem is given in Quantitative Aptitude which is a very essential paper in teaching exam. Given below are some more example of practising.

**Formula:**

- Average: = (Sum of observations / Number of observations).

**Find the Average Speed**

- 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 at x km/hr and B km at y km/hr and C km at z km/hr, then the average speed in covering the whole distance is-
**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 separated person – (Decrease in average × total number of persons)

Age of new person

**When a person joins the group-****In case of increase in average**

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

**In case of a decrease in average**

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

**In the Arithmetic Progression, there are two cases when the number of terms is odd and the second one is when the number of terms is even.**

- So 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.

__Some Important Examples__

__ __**Examples 1:** what will be the average of 13, 14, 15, 16, 17?

**Solution**: Average is the middle term when the number of terms is odd, but before that let’s checks whether it is in A.P or not since the common difference is same so the series is in A.P. So the middle term is 15 which is our average of the series.

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

**Solution:** We have discussed that when the number of terms is even then the average will be the average of **two middle terms.**

Now the two middle terms are 15 and 16, but before that the average we must check that the series should be A.P. Since the common difference is same for each of the term we can say that the series is in A.P. and the average is (16+15)/2 = 15.5

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

**Answer** :

let the excluded number is

= (29 x 5) – ( 27 x 4 )

= 145 – 108

= 37.

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

**Answer:**

**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 .**

**Answer**:

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.

**Thanks**

**Prep Smart. Score Better. Go Gradeup.**