Average MCQ Quiz - Objective Question with Answer for Average - Download Free PDF

Sum of weights of teacher and principal

⇒ New avg. × No. of students – Existing avg. × No. of students

⇒ 36.76 × 50 – 36 × 48 = 1838 – 1728

⇒ 110 kg

∴ Sum of weight of teacher and principle is 110 kg

Given:

Number of teacher = 20 

The average age of all teacher = 50 years

Concept used:

Average = (The sum of N number/N)

Calculation:

Let the age of the new teacher be x.

Number of teacher = 20 

The average age of all teacher = 50 years

⇒ Total = 20 × 50

⇒ 1000

Now a 40-year teacher left the group 

⇒ 1000 - 40 

⇒ 960

After joining the new teacher the average increases by 1.

⇒ Now, Total = 51 × 20

⇒ 1020

The age of new teacher

⇒ 1020 - 960

⇒ 60

∴ The age of the new teacher is 60 years.

Number of teacher = 20 

The average age of all teacher = 50 years

Age of teacher who leaves the group = 40 years

New average = 51

⇒ Age of new people = new total age - (old total age - 40)

⇒ Age of new teacher = 51 × 20 - (50 × 20 - 40)

⇒ 1020 - (1000 - 40)

⇒ 1020 - 960

⇒ 60

∴ The age of the new teacher is 60 years.

Age of teacher leaves the group = 40 years

Number of teachers in the group = 20 years 

Average increases = 1

Now, the age of the new teacher

⇒ 40 + 20 × 1

⇒ 60 

∴ The age of the new teacher is 60 years.

Given:

Average mark of 10 students = 25

New average mark after 1 more student joins = 24

Total students after new student joins = 11

Formula used:

Total marks = Average × Number of students

Mark of new student = Total marks after new student joins - Total marks of original group

Calculation:

Total marks of original group = 25 × 10

⇒ Total marks of original group = 250

Total marks after new student joins = 24 × 11

⇒ Total marks after new student joins = 264

Mark of new student = Total marks after new student joins - Total marks of original group

⇒ Mark of new student = 264 - 250

⇒ Mark of new student = 14

∴ The correct answer is option (2).

Given:

The average weight of P, Q & R= 55 Kg

The average weight of P & Q = 50 Kg

The average weight of Q & R = 53 Kg

Concept used:

Sum of n object = Average of n object × Number of object

Calculation:

Sum of weight(P+Q+R)= 55 × 3=165 kg

Sum of weight(P+Q)= 50 × 2= 100 kg

Sum of weight(Q+R)= 53 × 2= 106 kg

Weight of Q

⇒ {Sum of weight(P+Q) + Sum of weight(Q+R)} - Sum of weight(P+Q+R) 

⇒ {100 + 106} - 165

⇒ 41 kg

 ∴ The correct answer is 41 kg.

Given:

Average weight of 24 persons = 34 kg

Average weight of 48 persons = K kg

Average weight of all 72 persons = 56 kg

Formula used:

Average weight =

Calculations:

Let total weight of 24 persons = 24 × 34 = 816 kg

Let total weight of 48 persons = 48 × K = 48K kg

Total weight of 72 persons = 72 × 56 = 4032 kg

So, total weight = 816 + 48K = 4032

⇒ 816 + 48K = 4032

⇒ 48K = 4032 - 816

⇒ 48K = 3216

⇒ K =

⇒ K = 67 kg

∴ The correct answer is K = 67 kg.

Given:

The average weight of P and his three friends = 55 kg

The weight of P = 4 kg more than the average weight of his three friends

Formula used:

The total sum of the terms = Average × Number of terms

Calculation:

The total weight of P and his three friends = 55 × 4 = 220 kg

Let, the average weight of three friends = x

So, the total weight of three friends = 3x

The weight of P = x + 4

Then, (x + 4) + 3x = 220

⇒ 4x + 4 = 220

⇒ 4x = 220 - 4 = 216

⇒ x = 216/4 = 54

∴ P's weight = 4 + 54 = 58 kg

∴ The P's weight (in kg) is 58 kg

Given:

Total students = 20

19 students spent = 175 each

Formula used:

Average cost = Total cost/total number of person

Calculation:

Let the 20th student spend = X

According to the question:

⇒ (19 × 175 + X)/20 = X - 19

⇒ (3325 + X) = 20 × (X - 19)

⇒ 3325 + X = 20X - 380

⇒ 19X = 3325 + 380 = 3705

⇒ X = 3705/19 = Rs.195

Total money spent at hotel = (19 × 175) + 195 

⇒ 3325 + 195 = Rs.3520

∴ The correct answer is Rs.3520.

 Alternate Method

Total Student = 20

Let Avg spend by 20 students = y

Total spend = 20y

⇒ 20y = 19 × 175 + (y + 19)

⇒ 19y = 3344

⇒ y = 176

Total spend = 20 × 176

∴ Total money spent by them is Rs. 3520

Let age of P, Q, R and S be P, Q, R and S respectively.

Given,

⇒ P + Q + R = 24 × 3

⇒ P + Q + R = 72

Then,

⇒ P + Q + R + S = 30 × 4 = 120

⇒ S = 120 - 72 = 48 Years

The age of S is 48 years.

⇒ T = 48 + 4 = 52 years

Total age of five persons =

= 120 + 52

= 172

Average age of 5 persons = 172/5 = 34.4 years

Given:

Average of 28 numbers = 77

Average of first 14 numbers = 74

Average of last 15 numbers = 84 

Formula used:

Average = Sum of observations ÷ No of observations

Calculation:

Value of 14th number = (Sum of first 14 numbers +  Sum of last 15 numbers) - Sum of 28 numbers  

⇒ 14th Number = (14 × 74 + 15 × 84 - 28 × 77)

⇒ 1036 + 1260 - 2156 = 140 

Average of remaining 27 numbers = (Sum of 28 numbers - 14th number) ÷ 27 

⇒ (2156 - 140) ÷ 27 = 2016 ÷ 27 

⇒ 74.66 or 74.7

∴ The required result = 74.7 
Alternate Method

Average of 28 numbers = 77

Average of first 14 numbers = 74

Average of last 15 numbers = 84

Deviation on first 14 numbers = 74 - 77 = - 3 × 14 = - 42 

Deviation on last 15 numbers = 84 - 77 = 7 × 15 = 105

14th number = 77 - 42 + 105 = 140

∴ Average of remaining 27 numbers = (28 × 77 - 140) ÷ 27 = 74.7

Given:

The batting average for 27 innings of a cricket player is 47 runs.

His highest score exceeds his lowest score by 157 runs.

If these two innings are excluded, the average of the remaining 25 innings is 42 runs.

Formula used:

Average run = Total run in total innings/Total number of innings

Calculation:

Sum of runs for 27 innings of a cricket player = 47 × 27 = 1269

Sum of runs for 25 innings of a cricket player = 42 × 25 = 1050

Sum of remaining 2 innings = 1269 - 1050 = 219

Let the minimum score be x and the maximum score be x + 157

According to the question,

x + x + 157 = 219

⇒ 2x = 219 - 157

⇒ 2x = 62

⇒ x = 31

So, highest score = 157 + 31

⇒ 188

∴ His highest score in an innings is 188.

Shortcut Trick

The batting average for 27 innings of a cricket player is 47 runs.

The batting average for 25 innings is 42 runs (High and Low score excluded)

Here, Average decreases by (47 - 42) = 5

So, Total runs in that two innings (H + L) = 47 + 47 + (25 × 5) = 219 runs

Difference of runs in that two innings (H - L) = 157 runs

So, 2H = 219 + 157

⇒ H = 376/2 = 188 runs

Given:

Average of nine numbers = 60

Average of first five numbers = 55 and average of next three numbers = 65

Tenth number = Ninth number + 10

Concept used:

Average = Total sum of all numbers / (Count of the numbers)

Calculation:

The sum of nine numbers = 60 × 9 = 540

The sum of the first five numbers = 55 × 5 = 275

The sum of the next three numbers = 65 × 3 = 195

Ninth number = (540 – 275 – 195) = (540 – 470) = 70

∴ Tenth number = 70 + 10 = 80

Mistake PointsWe have details about 10 numbers but the average is given only of 9 

numbers. To calculate the 10th number, we have a relationship that is

the ninth number is 10 less than the tenth number. So after calculating

the 9th number, use this relation to find the next number. Don't take

the average of 10th number. 

Given:

The average salary of the entire staff = Rs. 15000

The average salary of officers = Rs. 45000

The average salary of non-officers = Rs. 10000

Number of officers = 20 

Calculations:

Let the number of non-officers be x.

Total member in entire staff = x + 20

Total salary of the entire staff = (x + 20) × 15000

⇒ 15000x + 300000      ----(1)

Total salary of officers = 20 × 45000 = 900000

Total salary of non-officers = x × 10000 = 10000x 

Total salary of the entire staff = 900000 + 10000x      ----(2)

From equation (1) and (2)

⇒ 10000x + 900000 = 15000x + 300000

⇒ 5000x = 600000

⇒ x = 120

Alternate Method

The ratio of officers to non-officers = 5000 ∶ 30000 = 1 ∶ 6

Number of officers = 1 unit = 20

Then, number of non-officers = 6 unit = 120

Given:

Average of 40 numbers = 71

Formula:

Average = Sum of all observations/Total number of all observations

Calculation:

Sum of 40 numbers = 40 × 71 = 2840

New sum of 40 numbers = 2840 – 100 + 140 = 2880

New average of 40 numbers = 2880/40 = 72

∴ The average increased = 72 – 71 = 1

Shortcut Trick

New average = Old average + (Change in number/Total numbers)

New average of 40 numbers = 71 + (140 – 100)/40 = 71 + 1 = 72

∴ The average increased = 72 – 71 = 1 

Given:-

Average weight of 20 students = 54 kg

Average weight of 12 students = 52 kg

Average weight of 7 students = 56 kg

Formula used:-

Average = (Sum of all weight)/(Total no. of weight)

Calculation:-

According to question-

⇒ (Sum of 20 students)/20 = 54

⇒ Sum of 20 students = 54 × 20

⇒ Sum of 20 students = 1080

∴ Sum of 12 students = 52 × 12

⇒ Sum of 12 students = 624

⇒ Sum of 7 students = 56 × 7

⇒ Sum of 7 students = 392

Average of remaining students = (Sum of 20 students + Sum of 12 students - Sum of 7 students)/(20 + 12 - 7)

Average of remaining students = (1080 + 624 - 392)/25

Average of remaining students = 1312/25 = 52.48

∴ Average of remaining students is 52.48. 

Given:

The average of 45 data is 150

46 is wrongly written as 91

Concept used:

Average = Sum of total observations/Total number of observations

Calculation:

The total sum of all 45 number = 150 × 45 = 6750

Now, 46 is wrongly written as 91

The correct sum of data = 6750 – (91 – 46) = 6705

Then, Correct average of the data = 6705/45 = 149

∴ The correct average is 149

Difference between wrong and actual numbers = 91 – 46 = 45

As the actual number is less than the wrong number

So the average decreased by 45/45 = 1

The correct average = 150 – 1 = 149

∴ The correct average is 149