**CALCULATE AVERAGE SHORTCUT TRICKS**

You know that the quantitative
aptitude section is most important in **bank
exams in PO and** **Clerk** and for
other competitive exams because if you want a good score in the bank exam then you
have to score well in maths. In competitive exams the most important thing is
time management, if you know how to manage your time then you can do well in **Bank Exams.** That’s where maths shortcut
tricks and formulas are comes into action. So continuously we are providing
shortcut tricks on different maths topics.

One of the most important
topics in maths is average. You should know how to **calculate the Average** in a very short time. For this here we are
providing shortcut tricks to calculate averages in maths.

**AVERAGE:**An average, or more accurately an arithmetic mean is, in crude terms, the sum of n different data divided by n.

**HOW TO CALCULATE THE AVERAGE:**

For example, if a batsman scores
30, 50, and 25 runs in the first, second, and third innings respectively, then his
average runs in 3 innings is equal to

30+50+25/3; =39 runs

**Therefore, the two most used formulas in this question are:**

Average= total of data/no. of
data

And total = average × no. of data

**Important Formulae Related to Calculate Average of numbers:**

1.
Average of first n natural number = (n+1)/2

3.
Average of first n odd number = n

4.
Average of consecutive number = (First number +Last number)/2

5.
Average of 1 to n odd numbers = (Last odd number+1)/2

6.
Average of 1 to n even numbers = (Last even number+2)/2

7.
Average of squares of first n natural numbers = [(n+1) (2n+1)]/6

8.
Average of the cubes of first n natural number = [n (n+1) ^2]/4

9.
Average of n multiples of any number = [Number*(n+1)]/2

**Examples with shortcut tricks on how to calculate Average are given below:**

**1. Ex: the average age of 30 boys in a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher?**

**Solution:**total ages of 30 boys = 14 × 30 = 420yrs.

Total ages when class teacher is
included = 15 × 31 = 465yrs.

So the age of the class teacher = 465 –
420 = 45 yrs.

**Shortcut trick:**age of new entrant = new average + no. of old members × Increase in average = 15 + 30 (15-14) = 45 yrs.

**2. Ex: the average weight of 4 men is increased by 3 kg when one of them who weighs 120kg is replaced by another man. What is the weight of the new man?**

**Solution:**

**by shortcut trick:**if the average is increased by 3 kg, then the sum of weight increases by 3 × 4 = 12 kg.

And this increase in weight is
due to the extra weight included due to the inclusion of new person.

So weight of new man = 120 + 12 =
132 kg.

We can also solve this question
by Direct formula: weight of new person = weight of removed person+ no. of
persons × increase in average = 120 + 4 * 3= 132 kg.

**3. Ex: the average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed the examination?**

**Solution:**Let the number of passed candidates be x.

The total marks = 120 × 35 = 39x
+ (120-x) * 15

Or, 4200 = 39x + 1800 – 15x

Or, 24x = 2400

X = 100

So the number of passed candidates =
100.

**We can also solve this question by shortcut trick direct formula:**

Number of passed candidates =

total candidates ( total average –
failed average) / passed the average-failed average

And the number of failed candidates=

Total candidates (passed average –
total average) / passed average – failed average

by this, we can solve the number of
passed candidates = 120 (35 – 15) / 39 – 15

= 100

**4. Ex: A batsman in his 17**

^{th}innings makes a score of 85, and thereby increases his average by 3. What is his average after 17 innings?**Solution:**let the average after 16

^{th}innings be x, then 16x + 85

= 17 (x + 3) = Total score after
17

^{th}innings.
X = 85 – 51 = 34

Average after 17 innings = x + 3
= 34 + 3 = 37

**Shortcut tricks or direct formula:**

Average after 16 innings = 85 – 3
* 17 = 34

Average after 17 innings = 85 – 3
(17 – 1) = 37.

**5. Ex: a cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?**

**Solution:**total of 10 innings = 21.5 × 10 = 215

Suppose he needs a score of x in
11

^{th}innings; then average in 11 innings = 215 + x / 11 =24
Or x, = 264 – 215 = 49

**Shortcut tricks or direct formula:**

Required score = 11 × 24 – 21.5 ×
10 = 49

Note: the above formula is based
on the theory that the difference is counted due to the score in the last innings.

**6. Ex: in a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. Find the age of the new boy.**

**Solution: Shortcut trick:**

Age of new person = age of
removed person – no. of persons × decrease in average age

= 18 – 20 × 2/12

= 18 – 10/3

= 44/3

= 14 yrs 8 months.

**Also, read maths study notes & shortcut tricks on these topics:**

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