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Given:

Total numbers of boys = 10

Height of 4 boys = 1 m 40 cm = 140 cm

Height of 3 boys = 1 m 62 cm = 162 cm

Height of rest boys = 1 m 73 cm = 173 cm

Formula used :

Average = (sum of total observations)/(total numbers of observations) 

Calculation:

Total numbers of boys = 10

Numbers of rest boys = 10 – 4 – 3 = 3 boys

Sum of  height first 4 boys = 4 × 140 cm

⇒ Sum of  height first 4 boys = 560 cm

Sum of  height 3 boys = 3 × 162 cm

⇒ Sum of  height 3 boys = 486 cm

Sum of  height rest 3 boys = 3 × 173 cm

⇒ Sum of  height rest 3 boys = 519 cm

Total height of 10 boys = (560 + 486 + 519) cm

⇒ Total height of 10 boys = 1565 cm

Average = (sum of total observations)/(total numbers of observations) 

⇒ Average of height of 10 boys = (1565)/10

⇒ Average of height of 10 boys = 156.5

∴ Average of height of all boys is 156.5.

Given:

Average monthly savings during May = Rs. 750

Average monthly savings during June = Rs. 824

Average monthly savings during July = Rs. 775

Concept used:

Average = sum of months / number of months

Calculation:

The average monthly savings for the three months = (750 + 824 + 775)/3  =783

⇒ Rs. 783

∴ The average monthly savings for the three months is Rs. 783.

Given:

Father’s age = 45

Mother’s age = 42

Average age of two sibling = 15

Age of third sibling = 4 + Average age of all three siblings

Average age of family = 40

Formula used:

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

Calculations:

Let the average age of three siblings be ‘x’ and the average age of grandparents be ‘g’.

Age of third sibling = x + 4

Sum of age of two siblings = 15 × 2 = 30

⇒ [30 + (x +4)]/3 = x

⇒ 30 + x + 4 = 3x

⇒ 2x = 34

⇒ x = 17

Total age of siblings = 3x = 51

Average age of family = 40 = (45 + 42 + 51 + 2g)/7

⇒ 138 + 2g = 280

⇒ 2g = 142

⇒ g = 71

∴ The average age of grandparents is 71 years

GIven :

Age of Raman's wife = 50 years 

Age of Raman is 40% more than his wife 

Formula used :

Average = total value of all observations/Number of observations 

Calculations :

Raman's age = 50 + 40% of 50 = 70 years

Total sum of the age of Raman and his wife = 50 + 70 = 120 years 

Average of their age = 120/2

⇒ 60 years 

∴ The average of age of Raman and his wife is 60 years

Given:

Average height of 5 girls = 1 m 67 cm = 167 cm.

Two girls of height 1 m 56 cm and 1 m 69 cm leaves the group.

Formula used:

Average of numbers = (sum of all observations)/(total numbers of observations)

Calculation:

Sum of all observations = (average of numbers) × (total numbers of observations)

Average height of 5 girls = 167 cm

Sum of height of 5 girls = 167 × 5

⇒ Sum of height of 5 girls = 835 cm

Two girls left the group, Total sum of height two of girls = 156 cm + 169 cm

⇒ Total sum of height two of girls = 325 cm

Total sum of height of remaining 3 girls = ( 835 – 325)

⇒ Total sum of height of remaining 3 girls = 510 cm

Average of numbers = (sum of all observations)/(total numbers of observations)

So, Average of height of three girls = 510/3

⇒ Average of height of three girls = 170 cm

∴ Average of height of three girls is 170cm.

Given:

The given numbers are 125, 200, 325, 625, 225 and 120.

Formula used:

Average = (sum of total observations)/(total numbers of observations)

Calculation:

sum of total observations = 125 + 200 + 325 + 625 + 225 + 120 = 1620

Average = (sum of total observations)/(total numbers of observations)

⇒ Average = 1620/6 = 270

∴ The average of the numbers is 270.

GIVEN:

No of people = 71

Eldest - youngest = 35 years

Change in average without eldest = 3% decrease

Change in average without youngest = 2% increase

FORMULA USED:

Average = sum of all observations/total no of observations

CALCULATION:

Let original average age be x years

Age of eldest person = a years

Age of youngest person = b years 

A.T.Q

97% of x = (71x - a )/70

⇒ 97% of 70x + a = 71x      ----(1)

Also, 102% of x = (71x - b)/70

⇒ 102% of 70x + b = 71x      ----(2)

Equating (1) and (2)

97% of 70x + a = 102% of 70x + b

⇒ 5% of 70x = a - b

∴ 5% of 70x = 35 (a - b = 35)

5/100 × 70x = 35

⇒ x = 10 years

∴ The average age was 10 years

Given:

The average age of 6 brothers = 15 years

The age of youngest brother = 5 years

Formula used:

Average = sum of the ages/number of persons

Calculations:

Sum of the 6 persons = 6 × 15

⇒ 90

When the youngest brother born the sum of the remaining 6 brothers = 90 - 6 × 5

⇒ 90 - 30 = 60

Average of the group of brothers when the younger one born = 60/5

⇒ 12 years

∴ The average age of 6 members when younger one born is 12 years

At the time of birth, the age of the newly born baby is 0

So, the average age of 6 boys = 60/6 = 10 years

But here, no such option is available in the official paper so we have to consider at the time of birth of the baby number of boys = 5

And then their average age was 60/5 = 12 years.

If both 10 & 12 are available in option, then 10 will gate more priority.

Given

January, February and March income = Rs. 15,000; Rs. 25,000 and Rs. 20,000

Average expenses = Rs. 4,000

Formula used:

Average = Sum of all observation/Number of observation

Calculation:

Total income of January, February and March = Rs.(15,000 + 25,000 + 20,000)

⇒ Rs. 60,000

Total expenses of January, February and March = 4,000 × 3

⇒ Rs. 12,000

Saving of January, February and March = Rs.(60,000 – 12,000)

⇒ Rs. 48,000

Average saving = 48,000/3

⇒ Rs. 16,000

Given:

Average height of Anil, Binmal and Chander = 150 cm

Average height of Bimal and Chander = 90 cm

Formula used:

Average = Sum of all observation/Number of observation

Calculation:

(Anil + Bimal + Chander)/3 = 150

⇒ Anil + Bimal + Chander = 450     ----(1)

(Bimal + Chander)/2 = 90

Bimal + Chander = 180.     ----(2)

From (1) and (2)

Anil + 180 = 450

⇒ Anil = 270

∴ Anil’s height is 270 cm

Given:

The average of n numbers is 42. If 60% of the numbers are increased by 5 each and the remaining numbers are decreased by 10 each.

Concept used:

Average

Calculation:

Let the N number be 100 and their average is 42.

The average increases by 5 for 60% of numbers

New average : 42 + 5 = 47

Sum = 60% of 100 × 47 

Sum = 60 × 47 = 2820

For the remaining 40% average decreases by 10 each.

New average : 42 - 10 = 32

Sum = 40% of 100 × 32

Sum = 40 × 32 = 1280

Average = \(\frac{{2820\ +\ 1280}}{{100}}\)

Average = 41

GIVEN:

average of 15 observations = 29 

average of first 8 = 27 

average of last 8 = 31

FORMULA USED:

average = sum of all observations/total number of observations

CALCULATION:

sum of 15 observations = 15 × 29 = 435

sum of first 8 observations = 8 × 27 = 216

sum of last 8 observations = 8 × 31 = 248

the 8th observation is repeated twice in sum of first and last observations

8th observation = (sum of first 8) + (sum of last 8) - (sum of 15 observations) 

⇒ 216 + 248 - 435 = 29

∴ 8th observation is 29

Given:

Average of 27 numbers = 12

Average of first 13 numbers = 11

Average of last 13 numbers = 13

Formula used:

Sum of observations = average × Number of observations

Calculation:

Sum of 27 numbers = 12 × 27

⇒ 324

Sum of first 13 numbers = 11 × 13

⇒ 143

Sum of last 13 numbers = 13 × 13

⇒ 169

Total sum of first 13 numbers and last 13 numbers = (143 + 169)

⇒ 312

Now, 14th number = (324 – 312)

⇒ 12

∴ The 14th number is 12

Given:

Five consecutive months sale = Rs. 6,435, Rs. 6,927, Rs. 6,855, Rs. 7,230, Rs. 6,562

Six consecutive months average sale = Rs. 6,500

Formula Used:

Average = sum of values/number of values

Calculation:

Let sale of sixth month be Rs. x

Sum of sales of six consecutive months = Rs. (6435 + 6927 + 6855 + 7230 + 6562 + x)

⇒ Rs. (34009 + x)

Number of months = 6 

Average of sales of six consecutive months = Rs. (34009 + x)/6

⇒ Rs. 6500 = Rs. (34009 + x)/6

⇒ 6 × 6500 = 34009 + x

⇒ 39000 = 34009 + x

⇒ x = (39000 – 34009) 

⇒ x = 4991

∴ Rs. 4,991 sale must he have in the sixth month so that he gets an average sale of Rs. 6,500

Given∶

average number of bulbs produced by a company per day in a week is 500

Calculations∶

Let the number of bulbs produced by the company on 7 days of weeks is a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇ respectively.

Average of bulbs produced in the whole week = (a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇) / 7 = 500

⇒ a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇ = 3500

According to question; per day production is increased by 15% the total number of bulbs is ⇒ 3500 + 15% of 3500

⇒ 3500 + 525

⇒ 4025

New average = 4025 / 7

⇒ 575

Given: A factory has 130 workers. They were given certain scores based on their work. The average age of women is 14. The average age of men is 18. The average age of top 20 scorers is 17.

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

Calculation:

There are 70 men in the factory then

No. of women = 130 – 70 = 60

Average age of 60 women = 14

Average age of 70 men = 18

Average age of total workers in factory = [14 × 60 + 18 × 70]/130

⇒ (840 + 1260)/130

⇒ (2100/130) = 210/13

Let the average age of the last 110 scorers be x.

Average age of top 20 scorers = 17

So, the average age of 130 scorers is

210/13 = (20 × 17 + 110 × x)/130

⇒ 2100 = 340 + 110x

⇒ 110x = 1760

⇒ x = 176/11 = 16

Hence, the average age of the last 110 scorers is 16.

GIVEN:

The average of the scores obtained by Jitendra and Umar = 70, the scores obtained by Umar and Shyamal = 56, and the average of the scores obtained by Shyamal and Jitendra = 78

FORMULA USED:

Average = Sum of all Observation/Number of observation

CALCULATION:

Average = Sum of all Observation/Number of observation

⇒ Sum of scores of Jitendra and Umar = 70 × 2

⇒ Sum of the scores obtained by Umar and Shyamal = 56 × 2

⇒ Sum of the scores obtained by Shyamal and Jitendra = 78 × 2

⇒ Average of Jitendra, Umar, and Shyamal = (70 + 56 + 78)/3

⇒  Average of Score of Jitendra, Umar, and Shyamal = 204/3

⇒ 68

∴ The average Scores of Jitendra, Umar, and Shyamal is 68

Given:

the average of all the numbers between 7 and 56 that are divisible by 6

Concept used:

Average

Calculation:

Numbers between 7 and 56 divisible by 6

⇒ 12,18,24....54

All these numbers are in Arithmetic progression.

Common difference (d) = 6

Average of terms of AP = \(\frac{{\left( {a + l} \right)}}{2}\)

a is the first term and l is the last term.

Average : \(\frac{{12\ +\ 54}}{2} = 33\)

Second method:

Between 7 and 56 numbers which are divisible by 6 

⇒ 12,18,24...54

Common difference (d) = 6

Number of terms = \(\frac{{\left( {{\rm{Last\ term - First \ term}}} \right)}}{{{\rm{common \ difference}}}} + 1\)

Number of terms = \(\frac{{\left( {54 - 12} \right)}}{6} + 1\)

Number of terms (N) = 8

Sum of N terms = \(\frac{n}{2}\left( {a + l} \right)\)

Sum = 4 × (12 + 54)

Sum = 264

Average = Sum / Total number of terms

Average = \(\frac{{264}}{8}\) 

Average = 33

Given:

2 years ago, the average age of a family of 7 members was 16 years.

After the inclusion of a newborn baby, the present average age remains the same at 16 years.

Concepts used:

Average age = Sum of ages of all members in the family/Number of members in the family

Calculation:

Let the sum of the present age of all members be x.

So, Two years ago the sum of ages of all the members = x – (2 × 7) = (x – 14) years

The average age of family = (Sum of ages of all the members of the family)/(Number of members in the family)

⇒ 16 years = (x –  14)/7

⇒ x – 14 = 16 × 7

⇒ x – 14 = 112

⇒ x = 112 + 14

⇒ x = 126 years

A new baby is born in the family but the average age of family remains the same at 16 years today.

Let the age of newborn baby be y years.

Sum of ages of all members at present = x + y

⇒ (126 + y) years

Number of members at present in family = 8 

The average age of family = 16 = (126 + y)/8

⇒ 16 × 8 = 126 + y

⇒ y = (128 – 126) years

⇒ y = 2 years

∴ The age of new born baby is 2 years.

Given:

Two years ago, the average age of a family of 8 members was 18 years

 Formula used:

Average = sum of the observation/number of observation

Calculation:

2 year ago,

Average age of family = (2 × 8)/8

⇒ Average age of family 2 year age = 2

So, the average age of family = 18 + 2 = 20

According to the question,

After the born of baby, the average age of family is same today

So, number of family member is 9

Let the new born baby age be P years

⇒ 18 = [(20 × 8) + P]/9

⇒ 162 = 160 + P

⇒ P = 2

Given:

3 years ago average age of 5 members is 17 years.

Formula used:

Average = Sum of values/number of values

Calculation:

3 years ago average age of 5 members is 17 years

Sum of ages of 5 members, 3 years ago

⇒ 17 × 5 = 85

Average of Present age of 5 members = 20 years

Sum of present ages of 5 members = 20 × 5 = 100

But a baby born and average remains same i.e 17 years

Sum of present ages of 6 members = 17 × 6 = 102

Age of baby = 102 - 100 = 2 years

∴ The age of baby is 2 years.

Given:

Number of students = 70

Average score of girls is 40% more than boys

Concept used:

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

Calculation:

Number of boys and girls are 45 and 25

Let boys' average marks be 5x

Girls' average marks = 7x

45 × 5x + 25 × 7x = 120 × 70

⇒ 225x + 175x = 8400

⇒ 400x = 8400

⇒ x = 21

⇒ 5x = 105

⇒ 7x = 147

∴ Average score of boys and girls is 105, 147

Given:

Let total number of books inside a bag be N.

Total number of Red books = 40/100 × N = 2N/5

Total number of Green books = N - 2N/5 = 3N/5

⇒ 3N/5 = 60

⇒ N = 100

Total number of Red books = 2/5 × 100 = 40

Total price of Red books = 40 × 100 = Rs.4000

Total price of Green books = 60 × 120 = Rs.7200

Total price of 100 books = 4000 + 7200 = Rs.11200

∴ Average price of books inside a bag = 11200/100 = Rs.112

Given:

Run scored in 7 innings = 15

Runs scored in 7th innings = 21

Formula Used:

Average = Sum of all items / Number of items 

Calculation

Average run scored in 7 innings = (Total runs scored in 7 innings)/(Number of innings)

⇒ 15 = (Total runs scored)/7

By cross multiplication

⇒ Total runs scored in 7 innings = 105

Runs scored in 7^th inning = 21

Total runs scored in 6 innings = Total runs scored in 7 innings - Runs scored in 7^th inning

⇒ Total runs scored in 6 innings = 105 – 21

⇒ Total runs scored in 6 innings = 84

Average runs scored in 6 innings = (Total runs scored in 5 innings)/(Number of innings)

⇒ Average runs scored in 6 innings = 84/6

⇒ Average runs scored in 6 innings = 14

∴ Team scored average 14 runs in 6 innings.

Given:

Run scored in 6th inning = 18

The average run scored in 6 innings = 13

Formula Used:

Average = Sum of all items / Number of items 

Calculation:

The average run scored in 6 innings = (Total runs scored in 6 innings)/(Number of innings)

⇒ 13 = (Total runs scored)/6

By cross multiplication

⇒ Total runs scored in 6 innings = 78

Runs scored in 6^th inning = 18

Total runs scored in 5 innings = Total runs scored in 6 innings - Runs scored in 6^th inning

⇒ Total runs scored in 5 innings = 78 – 18

⇒ Total runs scored in 5 innings = 60

Average runs scored in 5 innings = (Total runs scored in 5 innings)/(Number of innings)

⇒ Average runs scored in 5 innings = 60/5

⇒ Average runs scored in 5 innings = 12

∴ The team scored average 12 runs in 5 innings.

The correct option is 2 i.e. 12 runs.

Given:

Average salary of 20 workers = Rs. 1900

Average salary of 20 workers and 1 manager = Rs. 2000

Formula used:

Total salary = Average salary × Number of persons

Calculation:

Total salary of 20 workers = 20 × Rs. 1900

⇒ Rs. 38,000

Total salary of 20 workers and 1 manager = Rs. 21 × 2000

⇒ Rs. 42,000

Salary of manager = Rs. 42,000 – Rs. 38,000

⇒ Rs. 4000

∴ The salary of manager is Rs. 4000

Given:

Total observation = 10

Average of 10 observation = 30

Average of 1^st six observation = 40

Average of last five observation = 20

Formula used:

Average = Total sum/Total number

Total sum = Average × Total number

Calculation:

The average of 10 observation = 30

30 = (Total sum of 10 observation)/10

Total sum of 10 observation = 30 × 10 = 300

Total sum of 1^st six observation = 40 × 6 = 240

Total sum of last five observation = 20 × 5 = 100

6^th observation is common in both 1^st and last

6^th observation = (Total sum of 1^st six observation + Total sum of last five observation) - Total sum of 10 observation

⇒ 6^th observation = (240 + 100) – 300

⇒ 340 – 300

⇒ 40

Given:

In two offices the average number of computers is 10. If 4 more computers are added to the 1^st office, the average number of computers in both the office will be 12. If 4 more computers are added to the 2^nd office, the 2^nd office would have double the number of computers than the 1^st one.

Formula:

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

Calculation:

Let x be the number of computers in 1^st office and y be the number of computers in 2^nd office

Then,

x + y = 20

Given, if 4 more computers are added to the 1^st office, the average number of computers in both the office will be 12

x + 4 + y = 12 × 2

x + 4 + y = 24      ----(1)

Given, if 4 more added to the 2^nd office, the 2^nd office would have double the number of computers than the 1^st one

y + 4 = 2x     ----(2)

Putting value of y + 4 in eq(1)

x + 2x = 24

x = 8

We know,

x + y = 20

8 + y = 20

Y = 12

So, computers in 2^nd office is 12

Given 

Mean marks of 60 student = 63

Mean marks of 40 other student = 60 

Formula Used 

Average = (sum of observation)/No. of observation 

Calculation 

Total marks by all student = 63 × 60 + 40 × 60 = 6180 

Average marks of all 100 students = 6180/100 = 61.8

∴ The required answer is 61.8 

Given - 

Number of Mango tree = 28

Number of Apple tree = 42

Number of Orange tree = 21

Solution - 

Let the minimum number of rows be n.

⇒ maximum number of plant in each row = HCF (28, 42, 21) = 7

⇒ minimum row = (28/7) + (42/7) + (21/7) = 4 + 6 + 3 = 13

∴ minimum number of row = 13.

Given:

Average wages in a week = Rs.630

Average wages for 5 days = Rs. 800

Formula Used:

Average = Sum of all items / Number of items 

Calculation:

Average wages of a week

⇒ Average wages = Sum of wages of a week/Number of days

⇒ 630 = Sum of wages of a week/7

⇒ 4410 = Sum of wages of a week                                    ………………… (1)

Average wages for 5 days

⇒ Average wages = Sum of wages for 5 days/Number of days

⇒ 800 = Sum of wages for 5 days/5

⇒ 4000 = Sum of wages for 5 days                                 …………………… (2)

Wages for 2 days = Wages of a week – Wages for 5 days

⇒ Wages for 2 days = 4410 – 4000

∴ Wages for 2 days = Rs. 410

The correct option is 4 i.e. Rs. 410

Given:

Total weight of 50 people group = 50 × 48 = 2400 kg

Total weight of 10 peoples = 10 × 45 = 450 kg

Total weight of 5 peoples = 5 × 50 = 250 kg

Total weight of 45 peoples = 2400 - 250 = 2150 kg

Total weight of (45 + 10 = 55) peoples = 2150 + 450 = 2600 kg

∴ Average weight of 55 peoples = 2600/55 = 47.27 ≈ 47 kg

Given:

Total number of customers on week days = 180 × 5 = 900

Total number of customers on weekend = 250 × 2 = 500

Total number of customers in a week = 900 + 500 = 1400

∴ Average number of customers in a week = 1400/7 = 200

Given:

Ram scored 40 marks

Radha scored 45 marks

Raj scored 35 marks

Calculation:

Let marks scored by Sham in semester exam be M.

Total marks obtained by four in semester exam = 40 + 45 + 35 + M = 120 + M

Total marks obtained by four in semester exam = 40.5 × 4 = 162

⇒ 162 = 120 + M

⇒ M = 42

∴ Difference between the marks obtained by Radha and Sham = 45 - 42 = 3

Concept used:
Average = (Sum of all terms)/(Number of terms)

Calculation:
10, 20, 30, 35, 40 & 45
Sum of terms = 10 + 20 + 30 + 35 + 40 + 45 = 180
Number of terms = 6
Average = 180/6 = 30
∴ The average is 30.

Given:

The average of 7 observation = 36

The average of another 13 observations = 46

Formula used:

Combined average/weighted average = Sum of observations/Total number of observation

Calculation:

Total of 7 observation = Average × 7 = 36 × 7 = 252

Total of 13 observations = Average × 13 = 46 × 13 = 598

Combined average = (36 × 7 + 46 × 13)/(7 + 13)

∴ Combined average = 850/20 = 42.5

Given:

The average of 12 numbers = 35

Formula used:

Average = Sum of values/number of values

Calculation:

The sum of 12 numbers

⇒ 35 × 12

⇒ 420

Each number multiplied by 2

The sum of numbers multiplied by 2

⇒ 420 × 2

⇒ 840

The New average of 12 numbers

⇒ 840/12

⇒ 70

∴ The required average is 70.

Given:

Average of 3 consecutive numbers = 15

Formula Used:

Average = Sum of terms/Number of terms

Calculations:

Let the 3 consecutive numbers be (x – a), x , (x + a).

Average of 3 consecutive numbers = 15

Average = Sum of terms/Number of terms

⇒ 15 = [(x – a) + x + (x + a)]/3

⇒ 15 × 3 = 3x

⇒ x = 15

3 consecutive numbers = (15 – a), 15, (15 + a)

Multiplying these numbers y 3, we get

Numbers = 3 × (15 – a), 3 × 15, 3 × (15 + a)

⇒ Numbers = (45 – 3a), 45, (45 + 3a)

Sum of these 3 consecutive numbers = (45 – 3a) + 45 + (45 + 3a)

⇒ Sum of these 3 consecutive numbers = 135

Number of terms = 3

Average = 135/3 = 45

∴ The new average when the three numbers are multiplied by 3 is 45.

Short Trick/Topper's Approach:

When all the terms are multiplied by a number, then the average is also multiplied by that number.

Average of 3 consecutive numbers = 15

All 3 numbers are multiplied by 3.

⇒ New average = 3 × 15 = 45 

∴ The new average when the three numbers are multiplied by 3 is 45.

Given

Numbers are 5, 8, 0, 12 and 15

Formula used

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

Calculation

The sum of all observations = 5 + 8 + 0 + 12 + 15 

⇒ 40

Number of observations = 5 

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

⇒ 40/5

⇒ 8

∴ The average is 8.

Given:

Average runs scored by 10 players = 35

Average if captain’s score is included = 35 + 2 = 37

Formula used:

Average runs = Sum of runs scored by the players/Number of players

Calculations:

Sum of runs scored by 10 players = 35 × 10

⇒ 350

If the score of the captain is included,

Sum of runs scored by 11 players = 37 × 11

⇒ 407

Runs scored by the captain = (Sum of runs scored by 11 players) – (Sum of runs scored by 10 players)

⇒ 407 – 350

⇒ 57

∴ The captain scored 57 runs

Given:

Average runs of 11 players = 60

Average runs of all players excluding the score by the captain = 60 + 5 = 65

Formula used:

Average of n numbers = Sum of all numbers/n

Calculation:

Total runs of the team = 11 × 60 = 660

Total runs of the team excluding the captain = 10 × 65 = 650

∴ Runs scored by the captain = 660 - 650 = 10

Given:

Each of Manu, Annu and kannu owns certain number of dogs. The average number of dogs with Manu and kanu is 19. The average number of dogs with Anu and kanu is 18. The number of dogs with Anu is 14.

Formula:

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

Calculation:

The average number of dogs with manu and kanu is 19

Total number of dogs with manu + kanu = 38

The average number of dogs with anu and kanu is 18

Total dogs with Anu + kanu = 36

Anu has 14 dogs then kanu has 36 – 14 = 22

Now,

manu + kanu = 38

If kanu has 22 then manu has 38 – 22 = 16 dogs

GIVEN:

Weight of the first type of rice = 25 kg

Price of the first type of rice = Rs. 48/kg

Weight of the second type of rice = 17 kg

Price of the second type of rice = Rs. 32/kg

CONCEPT:

Average cost = (total cost)/(total quantity) 

EXPLANATION:

The total cost of the first type of rice = 25 × 48 = Rs. 1200

The total cost of the second type of rice = 17 × 32 = Rs. 544

Total quantity = 25 + 17 = 42 kg

The average cost per kg = (1200 + 544)/42 ≈ Rs. 41.5

Given:

Average of 50 number is 36.

Formula used:

Average = Sum of values/number of values

Calculation:

Average of 50 number = 36

Sum of 50 number = 36 × 50 = 1800

Two number 63, and 65 discarded

Sum of left 48 numbers = 1800 - 63 - 65 = 1672

Average of Left 48 numbers

⇒ 1672/48

⇒ 34.83

∴ The average of remaining numbers is 34.83.

Given:

The average weight of B and C is 39 kgs. The average weight of A and B is 31 kgs

Formula:

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

Calculation:

The sum of weight of B and C = 39 × 2 = 78

The sum of weight of A and B = 62

Now,

B + C – A – B = 16

C – A = 16

Given:

Dhoni scored an average in the first 3 match = 120 runs per match

Dhoni scored an average in the last 4 match = 140 runs per match

Average runs per match for all the five matches = 122

Formula Used:

Average = (Total run)/Number of innings

Calculation:

Let the scores in the 5 exams be denoted by M1, M2, M3, M4, and M5

Dhoni’s average score in the first 3 matches = 120

M1 + M2 + M3 = 120 × 3 = 360

⇒ M1 + M2 + M3 = 360      ----(i)

Average in last 4 match = 140

M2 + M3 + M4 + M5 = 140 × 4

⇒ M2 + M3 + M4 + M5 = 560      ----(ii)

Average of all matches = 122 × 5

⇒ M1 + M2 + M3 + M4 + M5 = 610      ----(iii)

Subtracting (ii) form (iii), we get

⇒ M1 = (610 – 560) = 50

Subtracting (i) from (ii), we get

M4 + M5 – M1 = (560 – 360)

⇒ M4 + M5 = (200 + 50) = 250

Now, M1 + M4 + M5 = (50 + 250) = 300

Required average = 300 / 3

⇒ Required average = 100

Given:

The Sachin score runs in five inning is 57, 52, 102, 43, and 86

Calculation:

Let be assume average of Sachin's runs is x

⇒ x = (57 + 52 + 102 + 43 + 86)/5 = 340/5 = 68

∴ The required result will be 68.

Given:

The total number of pens with A, B and C is such that if they are distributed among 7 kids, each kid will get 13 pens. The average number of pens with B and C is 39.

Formula:

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

Calculation:

Pens were distributed among 7 kids and each kid get 13 pen

So, total pens = 13 × 7 = 91

Total pens with B + C = 39 × 2 = 78

Number of pens with A = 91 – 78 = 13

Given:

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

The above ratio can also be written as,

The students in the ratio of 16 : 20 : 25      ----(2)

Marks scored by the classes is in the ratio of 45 : 51 : 36      ----(3)

Assumption:

We can solve this question by taking any assumed ratio.

Let the assumed ratio be 40.

Calculation:

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

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

Third ratio is 36 which is -4 to 40 and number is 25 so we will multiply -4 * 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 average.