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GIVEN:

The students in the ratio of 144 : 180 : 225      ----(1)

Marks scored by the classes is in the ratio of 45 : 51 : 36      ----(2)

CONCEPT USED:

⇒ Ratio assumption & deviation method

CALCULATION:

The eq(1) can also be written as,

The students in the ratio of 16 : 20 : 25      ----(3)

Marks scored by the classes is in the ratio of 45 : 51 : 36      ----(4)

We can solve this question by taking any assumed ratio.

Let the assumed ratio be 40.

The first ratio is +5 to 40 and of 16 students so we will multiply +5 x 16 = 80      ----(4)

Second ratio is 51 which is +11 to 40 and number is 20 so we will multiply +11 x 20 = 220      ----(5)

Third ratio is 36 which is -4 to 40 and number is 25 so we will multiply -4 x 25 = -100      ----(6)

Adding eq(4), eq(5) and eq(6) and dividing by total numbers.

⇒ Deviation = (80 + 220 - 100)/61

⇒ Deviation = + 3.278

Adding this deviation to assumed average we get 43.278

⇒ Actual average = 43.278

Total weight of(36+44) students = (36*40+44*35) kg = 2980 kg. 

Therefore weight of the total class = (2980/80) kg = 37.25 kg

Let the third number be x. 

Then second number = 3x. 

First number=3x/2.

Therefore x+3x+(3x/2)=(44*3) or x=24 

So largest number= 2nd number=3x=72.

Given :

Number of friends having lunch together = 12

Eleven of them spent = Rs. 120 each

Calculation:

Let the average expenditure of 12 friends be x

⇒ 120 × 11 + (x + 44) = 12x

⇒ 1320 + x + 44 = 12x

⇒ 1364 = 11x

⇒ x = 124

∴ Total money spent = 12x = 12 × 124 = Rs. 1488.

The total money spent by 12 friends is Rs. 1488.

Let the average expenditure of all nine be Rs.x 

Then 12*8+(x+8)=9x or 8x=104 or x=13. 

Total money spent = 9x=Rs.(9*13)=Rs.117.

Given:

seven women each spent on food = Rs.4 

Eight women spent Rs.7 more than average of all eight women

Concept Used:

Average = Sum of all observation/Number of observation

Calculation:

Let the amount spent by the eighth women be x 

Total amount spent by 7 people = 4 × 7 = 28 

Total amount spent by 8 people = 28 + x 

Average amount spent by 8 people = (28 + x)/8

According to question

⇒ x - (28 + x)/8 = 7

⇒ (8x - 28 + x) = 56

⇒ (7x - 28) = 56

⇒ 7x = 56 + 28

⇒ x = 84/7

⇒ x = 12

Total amount = 28 + 12 = Rs. 40

∴ Total amount spent by 8 women is Rs.40

Given:

The average temperature of 3 days - Monday, Tuesday and Wednesday is 60°C.

The average temperature of Tuesday and Wednesday is 52.5° C.

The temperature on Wednesday was twice the temperature on Tuesday.

Concepts used:

Average temperature = (Sum of temperature on all days)/(Number of days)

Calculation:

Sum of temperature on Monday, Tuesday and Wednesday = 60°C × 3 = 180°

Sum of temperature on Tuesday and Wednesday = 52.5°C × 2 = 105°C

The temperature on Monday = Sum of temperature on Monday, Tuesday and Wednesday – Sum of temperature on Tuesday and Wednesday  

⇒ Temperature on Monday = 180°C - 105°C = 75°C

Let the temperature on Wednesday and Tuesday be x°C and y°C respectively.

⇒ x = 2y      ----(1)

So, x + y = 105°C      ----(2)

Putting the value of x from eq (1) into eq (2),

⇒ 2y + y = 105°C

⇒ 3y = 105°C

⇒ y = 35°C

⇒ x = 2y = 2 × 35°C = 70°C

⇒ Sum of temperature on Monday and Wednesday = 75°C + 70°C = 145°C

∴ The sum of temperature on Monday and Wednesday is 145°C.

Given:

Initial average = 16.75 years.

20 new persons with an average age of 13.25 years joined

New average = 15 yrs.

Formula:

Average of n numbers a1, a2, ………. an = (a1 + a2 + ... + an)/n

Calculation:

Let the no. of person initially going for the trip be x.

Total age of x persons = x × 16.75

Total age of 20 persons = 13.25 × 20 = 265

Total age of all the persons = 15 × (x + 20)

From the question

16.75x + 265 = 15(x + 20)

⇒ 16.75x + 265 = 15x + 300

⇒ 1.75x = 35

⇒ x = 20

∴ Initial number of person is 20

Given:

Average of 45 men is 30 years

Concept used:

Average = (Total of all the variables/ No. of variables)

Calculation:

Total age of 45 men = 45 × 30 = 1350 years

Total age of 50 men = 50 × 33 = 1650 years

Total age of 5 new men = 1650 – 1350 = 300 years

Average age of 5 new men = 300/5 = 60 years

∴ The average of ages of new 5 men is 60 years

Given:

The length and width of a rectangle are increased by 40% and 20% respectively

Total increased is 68%.

Formula used:

Area of rectangle = Length × Breadth

Calculation:

In the given question neither length given nor breadth is given but only increased percentage is given .

So, we don't have data to calculate length of the rectangle by about what percentage of the width

∴ We can't determine .

Given :

The ratio of boys and girls in class = 9 ∶ 7

the average weight of all boys and girls = 54.25 kg

the average weight of all girls = 52 kg

Concept used :

 \({Average\ weight}= {Total \ weight \over Total\ no.\ of\ people}\)

Calculation :

Let the no. of boys and girls be 9 units and 7 units

According to the question,

Total weight of all the boys and girls = 16 (units) × 54.25 kg

⇒ 868 kg

Also, the Total weight of all the girls = 7 (units) × 52 kg

⇒ 364 kg

⇒ Total weight of all the boys = Total weight of all the boys and girls - Total weight of all the girls

⇒ Total weight of all the boys = 868 - 364

⇒ Total weight of all the boys = 504 kg

⇒ The average weight of all the boys = Total weight of all the boys / Total number of boys

⇒ The average weight of all the boys = 504/9

⇒ 56

∴ The average weight of the boys is 56 kg

Given:

The avg of 7 numbers is 40 while the avg of 9 numbers is 48.

The ratio of the remaining 2 numbers is 3 ∶ 5.

Concepts used:

avg= Sum of all observations/Number of observations

Calculation:

Sum of 7 observations = 40 × 7 = 280

Sum of 9 observations = 48 × 9 = 432

Sum of remaining 2 observations = Sum of 9 observations – Sum of 7 observations

⇒ 432 – 280 = 152

Let the two numbers be 3x and 5x.

According to the question

⇒ 3x + 5x = 152

⇒ 8x = 152

⇒ x = 19

Larger number = 5x

⇒ 5 × 19 = 95

∴ The value of larger number between remaining two numbers is 95.

Given:

The ratio of three numbers = 5 ∶ 9 ∶ 11

The second number is greater than the average of first and third number by 3

Concept used:

Average = (Total sum)/(Total numbers)

Calculations:

Let the numbers be 5x, 9x, and 11x respectively

Average of first and third number = (5x + 11x)/2 = 8x

According to question

⇒ 9x = 8x + 3

⇒ x = 3

The largest number = 11x

⇒ 11 × 3 = 33

Given:

Average age of 11 cricket players = 25

The average age of 11 cricket players after coach’s age is included = 27

Concept used:

Average = (Total sum)/(Total numbers)

Calculations:

Let the age of coach be T

Initially, the average age = 25 years

Number of players = 11

Total of age for 11 players = 25 × 11 = 275 years

According to the question,

After adding the age of the coach, new average is obtained as:

⇒ (275 + T)/12 = 27

⇒ 275 + T = 27 × 12

⇒ 275 + T = 324

⇒ T = 324 – 275 = 49 years

∴ The age of the coach is 49 years

Given:

Average age of 11 players and a coach = 18 years

Average age of 11 players = 17 years

Formula used:

Sum of age = Average age × Number of players

Calculation:

Number of persons including 11 players and a coach = 12

Total age of 11 players and a coach = 18 × 12

⇒ 216 years

Total age of 11 players = 17 × 11

⇒ 187 years

Age of coach = (216 – 187) years

⇒ 29 years

∴ The age of coach is 29 years

Given:

15 mangoes at = 20 each

20 oranges at = 30 each

Concept:

Average = Total amount/Total number

Solution:

Total amount = (15 × 20) + (20 × 30) = 300 + 600 = 900

Total number of fruits = 15 + 20 = 35

Average = 900/35 = 180/7

Given-

Average of 15 numbers = 0. 

Concept Used-

Average = Sum of all the observations/Number of Observations

Calculation-

For the average of some numbers to be zero the sum of all the negative numbers should be equal to the sum of all the positive numbers.

Hence, in a set of 15 numbers we need at least one positive number which is equal to the sum of all other 14 negative numbers.

∴ At least one of the 15 numbers should be positive.

Given∶

The average of ages of Suman, Kanti and Reena is 30 years

six years from now the average ages of Suman and Kanti will be 36 years

Formula used ∶

Average = sum of all the observations / total number of observations

Calculations∶

Let the present ages of Suman, Kanti and Reena be S, K and R respectively

⇒ (S + K + R) / 3 = 30

⇒ S + K + R = 30 × 3

⇒ S + K + R = 90         ---(1)

Also six years from now the average ages of Suman and Kanti will be 36 years,

⇒ [(S + 6) + (K + 6)] / 2 = 36

⇒ S + K = 60         ---(2)

From (1) and (2) we get R = 30 years

Total sales done by the three teams = (67 + 72 + 48) × 6 = 1122

(Each team has 6 members including the team lead)

Average target sales of the company = 63

Total employees in the department(including Satish) = 6 × 3 + 1 = 19 

Target sales for the company = 63 × 19 = 1197

∴ Sales done by Satish to reach the target = 1197 – 1122 = 75

Given:

The mean of 6 observations = 12

New mean after adding two observations = 13

Calculation:

Sum of 6 observations = 6 × 12 = 72

Total observations after adding two more observations = 8

Sum of 8 observations = 8 × 13 = 104

Sm of two new observations = Sum of 8 observations - sum of 6 observations

Sum of teo new observations = 104 - 72 = 32

Mean of the two observations = 32/2 = 16

∴ Mean of two new observations is 16.

GIVEN:

average salary = RS 35000

increase in salary = RS 3000

CONCEPT:

if the salary of each employee increase or decrease by a particular amount the average also increases by the same amount

CALCULATION:

new average salary = 35000 + 3000 = RS 38000

Given:

The average salary per employee in the marketing department of MNC is Rs. 400.

The average salary of 10 senior employees = Rs. 550 per employee

The average salary of the remaining staff = Rs. 100 per employee.

Concepts used:

Average salary = (Total salary of all employees)/(Number of employees)

Calculation:

Let the total number of employees in the marketing department of MNC be x.

Total salary of all employees = Rs. 400 × x = Rs. 400x

Total salary of all senior employees = Rs. 550 × 10 = Rs. 5,500

Remaining staff = Total number of employees - Number of senior employees = x – 10

The average salary of the remaining staff is Rs. 100 per employee.

Total salary of remaining employees = Rs. (100x – 1,000)

Total salary of all employees = Total salary of all senior employees + Total salary of remaining employees

⇒ 400x = 5,500 + 100x – 1,000

⇒ 400x – 100x = 4,500

⇒ 300x = 4,500

⇒ x = 4,500/300

⇒ x = 15 employees

∴ There are total 15 employees working in the marketing department of MNC.

Given:

The average salary of all employees in a company = Rs. 5,000 per employee.

The average salary of all 15 employees of technical staff = Rs. 6,500 per employee

The average salary of Non-technical staff = Rs. 4,500 per employee.

Concepts used:

Average salary = (Sum of salaries of all employees)/(Number of employees)

Calculation:

Let the total number of employees in the company be x.

Sum of salaries of all employees = Rs. 5,000 × x = Rs. 5,000x

According to questions

Sum of salaries of technical staff = Rs. 6,500 × 15 = Rs. 97,500

Number of non-technical staff = x – 15  

So, Sum of salaries of non-technical staff = 4,500 × (x – 15) = 4,500x – 67,500

Sum of salaries of all employees = Sum of salaries of technical staff + Sum of salaries of non-technical staff 

⇒ 5,000x = 97,500 + (4,500x – 67,500)

⇒ 5,000x – 4,500x = 97,500 – 67,500

⇒ 500x = 30,000

⇒ x = 60

Number of non-technical employees = 60 – 15 = 45

∴ There are 45 non-technical employees in the company.

Solution:

Concept:

Average = (Sum of total score)/(Total innings)

Calculation:

Let be assume before inning was p

Total score of batsman was = 42 × p

Now, total inning is = p + 5

and, total score = 20 + 35 + 25 + 10 + 40 + (42 × p) = 130 + (42 × p)

Now average 

⇒ 42 - 5 = [130 + (42 × p)]/(p + 5)

⇒ p = 11

⇒ Total inning he play is = 11 + 5

⇒ 16

∴ The required result will be 16.

Given:

12th innings score = 90 runs

Formula used:

Average runs = Total runs/Number of innings

Calculation:

Let, the 11 innings average is x.

⇒ Total runs of 11 innings = 11x

⇒ (11x + 90)/12 = (x - 5)

⇒ 11x + 90 = 12x - 60

⇒ x = 150 runs

⇒ Current average = 150 - 5 runs

⇒ Current average = 145 runs

∴ The current average runs is 145 runs.

Given:

Runs scored by batsman in 12^th innings = 85 runs

Batting average increases by 4

Formula used:

Total runs scored = Average × Number of innings

Calculation:

Let average runs after 11^th innings be n

Batting average after 12^th innings = (n + 4)

Total run in 11 innings = 11n

According to the question

⇒ (11n + 85) = 12(n + 4)

⇒ 11n + 85 = 12n + 48

⇒ n = 37

Average after 12^th innings = (n + 4)

⇒ 37 + 4 = 41

Given:

Average of 13 results = 60

Average of 1^st 7 results = 59

Average of the last 7 result = 61

Formula Used:

Average = Sum/Number

Calculations:

As we know,

Average = Sum/Number

⇒ 60 = S/13

⇒ Sum = 780

⇒ Sum of 1^st 7 numbers = 59 × 7 = 413

⇒ Sum of last 7 numbers = 61 × 7 = 427

⇒ 7^th result = Sum of 1^st 7 numbers + Sum of last 7 numbers - Sum of all the results

⇒ (413 + 427 - 780)

⇒ 840 - 780

⇒ 60

Given:

Sum of four consecutive even numbers = 27 more than the average

Formula used:

Arithmetic mean = [(1st number + last number)/2]

Calculation:

Let 1st even number be n

So, other three numbers = (n + 2), (n + 4), (n + 6)

n + (n + 2) + (n + 4) + (n + 6) = [{(n  + (n + 6)}/2] + 27

⇒ 4n + 12 = n + 3 + 27

⇒ 3n = 30 – 12 

⇒ 3n = 18

⇒ n = 6

⇒ (n + 4) = 6 + 4

⇒ 10

∴ The second largest number is 10

Given:

60 fruits are distributed among 5 men, A, B, C, D and E. A got 5 more fruits than B. B got 10 more fruits than C. C got 15 less fruits than D and average number of fruits D and E got was 20.

Formula:

Average of n numbers a1, a2 ... an = (a1 + a2 + ... an)/n

Calculation:

60 fruits are distributed among 5 men

So, the average number of fruits = 60/5 = 12

Given:

The average credit score of certain number of graduate students = 400.

The average score of 4 junior students = 600

The average score of senior graduates = 200.

Concepts used:

Average credit score = (Sum of credit scores of graduates)/(Number of graduates)

Calculation:

Let the total number of graduates be x.

So, the sum of credit scores of graduates = 400x

Now, the sum of credit scores of junior graduates = 600 × 4 = 2,400

Number of senior graduates = x – 4

According to the question 

Sum of credit scores of senior graduates = 200 × (x – 4) = 200x – 800

Sum of credit scores of graduates = Sum of credit scores of graduates + Sum of credit scores of graduates

⇒ 400x = 2,400 + 200x – 800

⇒ 400x – 200x = 1,600

⇒ 200x = 1,600

⇒ x = 1,600/200 = 8

Number of senior graduates = x – 4 = 8 – 4 = 4 graduates

∴ There are 4 senior graduates.

Given:

The average weight of the students in a group was 75.4 kg. Later on, four students having weights 72.9 kg, 73.8 kg, 78.5 kg and 88.4 kg respectively, joined the group. As a result, the average weight of all the students in the group increased by 0.24 kg.

Concept used:

Average

Calculation:

Let us suppose that the total number of students are x.

So by using the formula for average:

\(\dfrac{{{\rm{Total\ weight\ of \ all\ students}}}}{x} = 75.4\)

Next we have that four students added to the class weighing

72.9 kg, 73.8 kg, 79.5 kg and 87.4 kg = 313.6 kg

Now the total number of students will be (x + 4)

And the average weight is increased by 0.24

So the new average weight is 75.4 + 0.24 = 75.64kg

Number of students are given by: 75.64 (x + 4)

So we have:

75.4x + 313.6 = 75.64 x + 75.64 × 4

- 0.24x = 302.56 – 313.6

\(x = \dfrac{11.04}{0.24}= 46\)

so total number of students initially were 46.

Formula used∶

Average = Sum of all observation / Number of observation

Calculation∶

Largest 3 digit number = 999

Largest 5 digit number = 99999

Average = (999 + 99999) / 2

⇒ 100998 / 2

Given∶

Average height of Kamlesh, Bimla and Alok = 120 cm

Average height of Kamlesh and Bimla = 125 cm

Formula used∶

Average = Sum of all observations / Number of observations

Calculation∶

(Kamlesh + Bimla + Alok) / 3 = 120

⇒ Kamlesh + Bimla + Alok = 360         ...(1)

(Kamlesh + Bimla) / 2 = 125

Kamlesh + Bimla = 250         ...(2)

From (1) and (2)

Alok + 250 = 360

⇒ Alok = 110

Given 

The mean of 20 values = 35 

Formula Used 

Mean = sum of observation/No. of observation 

Calculation 

New mean = 35 /5 = 7 

so Every observation = 7 

Added 2 in every observation 

so observation become = 7 + 2 = 9 

∴ The required answer is 9 

Given:

Average sales of a Gadget shopkeeper = 15 gadgets per week

Formula Used:

Percentage = (Final value – Initial value) / Initial value × 100

Calculation:

The average rate of percentage increase in both the cases- weekly and yearly will be the same. 

Annual percentage in sales = (21 – 15) / 15 × 100

⇒ Annual percentage in sales = 600 / 15

⇒ Annual percentage in sales = 40%

Given:

Average temperature of Bhopal in the first four days of July 2019 = 52 degrees

Average for the second, third, fourth, and fifth days = 55 degrees

The temperatures of the first and fifth days were in the ratio = 5 : 7

Formula Used:

Average = (Total temperature) / Number of days

Calculation:

Let the temperature on 1^st and 5^th July 2017 be 5x and 7x degrees respectively. 

Sum of temperature on 1^st, 2^nd, 3^rd, and 4^th days = (52 × 4)

⇒ 208      ----(i)

Sum of temperature on 2^nd, 3^rd, 4^th, and 5^th days = (55 × 4)

⇒ 220      ----(ii)

Subtracting (i) from (ii)

5^th – 1^st = 12 degrees. 

Then, 7x – 5x = 12

⇒ 2x = 12

⇒ x = 6

Since temperature on the 5^th July 2017 in Bhopal = 7x

⇒ Since temperature on the 5^th July 2017 in Bhopal = 7 × 6 = 42 degrees

Given:

Average of 11 numbers = 28

Average of first 5 numbers = 23

Average of next 5 numbers = 25

Formula used:

Sum of observations = Average × Number of observations

Calculation:

Sum of 11 numbers = 28 × 11

⇒ 308

Sum of first 5 numbers = 23 × 5

⇒ 115

Sum of next 5 numbers = 25 × 5

⇒ 125

Total sum of first 10 numbers = (115 + 125)

⇒ 240

11th number = (308 – 240)

⇒ 68

∴ The 11th number is 68

Given:

Average age of A and B 4 years ago was 20 years.

Today, average age of A, B and C is 30 years.

Calculation:

Average age = Sum of ages of all individuals/Number of individuals

Calculation:

Let the age of A, B and C be x years, y years and z years respectively.

So, Four years ago the age of A and B is (x – 4) and (y – 4) respectively 

Now, four year ago the average age of A and B = (x – 4 + y – 4)/2

⇒ 20 = (x + y – 8)/2

⇒ x + y = 40 + 8

⇒ x + y = 48      ----(1)

Today, the average age of A, B and C is 30 years.

Average age = Sum of ages of all individuals/Number of individuals

⇒ 30 = (x + y + z)/3

⇒ x + y + z = 30 × 3 years

⇒ x + y + z = 90 years      ----(1)

Subtracting eq (1) from eq (2),

⇒ x + y + z - (x + y) = 90 – 48 years

⇒ z = 42 years

C's current age = z = 42 years

⇒ C's age 5 years from now = 42 + 5 years = 47 years

∴ C's age 5 years from now is 47 years.

Given:

Total sum of 13 numbers = 13 × 48.5 = 630.5

Formula:

Average = Sum of numbers/Total numbers

Calculation:

Total sum of first 5 numbers = 5 × 56.4 = 282

Total sum of last 9 numbers = 9 × 45.6 = 410.4

∴ 5th number = (282 + 410.4) - 630.5 = 61.9

Given:

Average age of 14 people = 50

Calculations:

Total age of all the people in the family = 50 × 14 = 700

Newborn joins the family and 4 years later the total age of all the members = 700 + (15 × 4)

⇒ 700 + 60

⇒ 760

∴ Required average = 760/15

⇒ 50.6

The average age after 4 years is 50.6.

Given :

Total of 500 people live in a society 

Their average age is 30 years 

125 people go out for a holiday 

Formula used :

Average = Total value of all observations/Number of observations 

Calculations :

Sum of the age of all people = 500 × 30 = 15000 years 

Remaining people who stays at society = 500 - 125 = 375 

Sum of the age of remaining people = 375 × 32  (Age increased by 2 years)

⇒ 12000 years 

Sum of age who left for vacation = 15000 - 12000 

⇒ 3000 

The average age of people left for vacation = 3000/125 

⇒ 24 years 

∴ The average age of the people who leave for vacation is 24 years

Solving for Quantity I:

Given:

Average of weight of 5 people in a room = 50 kg.

Average of weight of 6 people inside the room = 52 kg.

Formula used:

Average = (Sum of values)/(Number of values)

Calculations:

Let the average of 5 persons be x₁, x₂, x₃, x₄, x₅

(x₁ + x₂ + x₃ + x₄ + x₅)/5 = 50

⇒ x₁ + x₂ + x₃ + x₄ + x₅ = 250

After one person entered the room,

(x₁ + x₂ + x₃ + x₄ + x₅ + x₆)/6 = 52

⇒ x₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 312

⇒ x₆ = 312 – 250

⇒ x₆ = 62

∴ Weight of the person entered in room is 62 kg.

Solving for Quantity II:

Given:

Runs in four matches = 23, 27, 33, 47

Formula used:

Average = (Sum of values)/(Number of values)

Calculations:

Let he make x runs in last match to make average 40.

(23 + 27 + 33 + 47 + x)/5 = 40

130 + x = 200

x = 200 – 130

x = 70

∴ He has to make 70 runs to make his average 40

∴ Quantity I < Quantity II

Given:

The average age of 30 girls = 13

The average age of the first 13 girls = 15

Calculations:

Total age of 30 girls = 30 × 13

⇒ 390

Total age of 18 girls = 15 × 18

⇒ 270

∴ age of the remaining 12 girls = 390 – 270

⇒ 120

∴ required average = 120/12

⇒ 10 years

The average age of the remaining 12 girls is 10 years.

(a + b + c)/3 = 7

⇒ 4 + b + 10 = 21

⇒ b = 21 – 14 = 7

(b + c + d)/3 = 10

⇒ 7 + 10 + d = 30

⇒ d = 30 – 17

⇒ d = 13

Quantity I: (b + d) = 7 + 13

⇒ 20

Quantity II: (a + c) = 4 + 10

⇒ 14

∴ Quantity I ˃ Quantity II

Quantity I:

Let the numbers be 1x, 4x and 2x

⇒ (x + 4x + 2x)/3 = 14

⇒ (7x/3) = 14

⇒ x = (14 × 3)/7

⇒ x = 6

Largest number = 4x = 4 × 6 = 24

Quantity II: 34

∴ Quantity I ˂ Quantity II

Given:

The average of 12 numbers = X

Formula used:

Average = sum of observation/no. of observation

Calculation:

Average of the 12 numbers = X

Sum of the 12 numbers =  12X

Decrease of 1 number = 5 

Decrease of 12 numbers = 12 × 5 = 60 

Sum of the new 12 numbers = 12x - 60 

Average of new 12 numbers = (12x - 60 )/12 = x - 5

∴ The new average is x - 5.

Given:

50% of the parents donated an average of Rs. 1200

60% of the total donation = Donation of 50% of the parents

Formula used:

Total = Average × Number of observations

Calculation:

Let total parents be 100, and total donation be Rs. x

50% of total parents = 50% of 100 = 50

Total amount paid by 50 parents = 1200 × 50 = 60000

60% of the total donation = 60000

⇒ 60% of x = 60000

⇒ x = 100000

Remaining amount = Total amount – 60000

⇒ Remaining amount = 100000 – 60000 = 40000

This amount is to be paid by 50 parents

The average amount to be paid by the rest of the parents (i.e. 50) = 40000/50 = Rs. 800

∴ The average amount to be paid by the rest of the parents is Rs. 800

Given:

In a class there are three groups A, B and C.

One student from group A and two students from group B are shifted to group C

Formula used:

Average weight = total weight/Total student

Calculation:

According to the question:

No student going out of the class and No new student coming in the class

Total student weight same all the time and total no. of the same .

They are just interchange the group.

∴ The average weight of the students of the class the same.

GIVEN:

The average of twenty-five numbers is 54 and The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2

FORMULA USED:

Average = sum of the observation/Number of the observation

CALCULATION:

Average = sum of the observation/Number of the observation

⇒ Sum of the 25 numbers = 54 × 25 = 1350

⇒ Sum of the first 13 numbers = 13 × 52.8 = 686.4

⇒ Sum of the last 13 numbers = 13 × 62.2 = 808.6

⇒ 13^th number = (Sum of the first 13 numbers + Sum of the last 13 numbers) - (Sum of the 25 numbers)

⇒ (686.4 + 808.6) - (1350)

⇒ 1495 - 1350 = 145

⇒ Sum of the remaining 24 numbers = (1350 - 145) =1205

⇒ Average of the remaining 24 numbers = 1205/24 = 50.2

∴The average of the remaining 24 numbers is 50.2