# Maths Science Corner

# Maths

## Daily Quiz

# Average

# Paper Set 4

These posts are made precisely to give you the best shortest possible solution of all the questions.

Solutions cover variety of topics which are listed below :

**Mathematics**

Number System

LCM and HCF

Simplification

Power, Indices and Surds

Average

Ratio and Proportion

Percentage

Profit and Loss

Discount

Simple Interest

Compound Interest

Time and Work

Pipe and Cistern

Time and Distance

Boat and Stream

Sequence and Series

Algebra

Trigonometry

Geometry

Mensuration (2 - D and 3 - D)

Statistics and Data interpretation

**Reasoning**

Analogy or Similarity

Blood Relationship

Symbols and Notations

Classification

Direction and Distance tests

Schedule day/date/time

Series

Coding - Decoding

Word formation

Syllogism, Statement and Conclusions

Ranking and Arrangement

Finding the missing Number

Arithmetical problems

Arrangement of words in logical order

Cubes and Dice

Logical Venn Diagram

Series

Mirror Images

Water Images

Paper cutting and folding

Completion of figures

Embedded Figure

Deviation of figure

We will try to cover above all types of questions. So, keeping in touch with us will give you chance to crack various Government and Other Exams.

__Points to Remember for Average__

Rule 1 : Average of two or more numbers/quantities is called the mean of these numbers, which is given by Average(A) = Sum of observation (quantities) / No of observation (quantities)

Rule 2 : If the given observations (x) are occurring with certain frequency (A) then,

Average = (A1x1 + A2x2 + … + Anxn) / (x1 + x2 + xn)

where, A1, A2, A3. .......... An are frequencies

Rule 3 : The average of ‘n’ consecutive natural numbers starting from 1 i.e. Average of 1,2,3, .....n = (n +1)/2

Rule 4 : The average of squares of ‘n’ consecutive natural numbers starting from 1 is

[(n +1)(2 +1)]/6

Rule 5 : The average of cubes of first ‘n’ consecutive natural numbers is

[n(n +1)^2]/4

Rule 6 : The average of first ‘n’ consecutive even natural numbers i.e. Average of 2, 4, 6, ..... 2n = (n + 1)

Rule 7 : The average of first ‘n’ consecutive odd natural numbers i.e. 1, 3, 5, ..... (2n – 1) = n

Rule 8 : The average of certain consecutive numbers a, b, c, ......... n is (a + n)/2

Rule 9 : The average of 1st ‘n’ multiples of certain numbers x = [x(1 + n)]/2

Rule 10 : If the average of ‘n1’ numbers is a1 and the average of ‘n2’ numbers is a2, then average of total numbers n1 and n2 is Average = [n1a1 + n2a2]/(n1 + n2)

Rule 11 : If A goes from P to Q with speed x km/h and returns from Q to P with speed y km/h, then the average speed of total journey is Average speed = 2xy/(x + y) = total distance / total time taken

Rule 12 : If a distance is travelled with three different speeds a km/h, b km/h and c km/h, then Average speed of total journey = 3abc/(ab+ bc +ca) km/h

Rule 13 : If the average of m numbers is x and out of these ‘m’ numbers the average of n numbers is y. (or vice versa) then the average of remaining numbers will be

(i) Average of remaining numbers = (mx – ny)/(m – n) (if m > n)

(ii) Average of remaining numbers = (ny – mx)/(n – m) (if n > m)

Rule 14 : In three numbers, if 1st number is ‘a’ times of 2nd number and ‘b’ times of 3rd number and the average of all three numbers is x, then 1st number = [(3ab)/(a + b + ab)] x.

Rule 15 : From three numbers, first number is ‘a’ times of 2nd number, 2nd number is ‘b’ times of 3rd number and the average of all three numbers is x, then,

First number = [(3ab)/(1 + b + ab)] x

Second number = [(3b)/(1 + b + ab)] x

Third number = [(3b)/(1 + b + ab)] x

Rule 16 : If from (n + 1) numbers, the average of first n numbers is ‘F’ and the average of last n numbers is ‘L’, and the first number is ‘f’ and the last number is ‘

*l*’ then f –*l*= n(F – L)
Rule 17 : ‘t’ years before, the average age of N members of a family was ‘T’ years. If during this period ‘n’ children increased in the family but average age (present) remains same, then, Present age of n children = n.T – N.t

Rule 18 : If in the group of N persons, a new person comes at the place of a person of ‘T’ years, so that average age, increases by ‘t’ years.

Then, the age of the new person = T + N.t

If the average age decreases by ‘t’ years after entry of new person,

then the age of the new person = T – N.t

Rule 19 : The average age of a group of N students is ‘T’ years. If ‘n’ students join, the average age of the group increases by ‘t’ years,

then Average age of new students = T - [N/n + 1] t

If the average age of the group decreases by ‘t’ years,

then Average age of new students = T - [N/n + 1] t

Rule 20 : If the average of ‘n’ observations is ‘x’ and from these the average of 1st ‘m’ observations is ‘y’ and the average of last ‘m’ observations is ‘z’

then mth observation = m(y + z) – nx

(m + 1)th observation = nx – m(y + z)

Rule 21 : If the average age (height) of ‘n’ persons is x year (cms) and from them ‘m’ persons went out whose average age (height) is ‘y’ years (cms) and same number of persons joined whose average age (height) is ‘z’ years (cms) then what is the average age (height) of n persons ?

Average age = [x – {m(y – z)}/ n ] years (cms).

Rule 22 : Average of bowler = Total runs / No.of wickets

Total runs = Average (A). y, where y = Number of wickets.

Rule 23 : If in a group, one member is replaced by a new member,

then, Age of new member = (age of replaced member) ± xn

where, x = increase (+) or decrease (–) in average, n = Number of members.

Rule 24 : If a new member is added in a group

then, age (or income) of added member = Average (or income) ± x (n + 1)

where x = increase (+) or decrease (–) in average age (or income) n = Number of members.

Rule 25 : If a member leaves the group,

then income (or age) of left member = Average income (or age) ± x (n – 1)

where, x = increase (+) or decrease (–) in average income (or age) n = Number of members.

Rule 26 : If average of n numbers is m later on it was found that a number ‘a’ was misread as ‘b’.

The correct average will be =m + (a – b)/n

Today we are going to give you the Paper Set of #Average question of #Dailyquiz in #Maths asked earlier in various competitive Examinations. Yoy can follow Maths Science Corner on Facebook page, Twitter and Telegram. Enjoy the Paper Set and keep learning.

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