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

Given:

Average of (x + 5) numbers = 37.81

Average of (x − 2) numbers = 48

Remaining 7 numbers average = 32

Formula used:

Average = Sum ÷ Number

Total Sum = Average × Total Count

Calculations:

Sum of (x + 5) numbers = 37.81 × (x + 5)

Sum of (x − 2) numbers = 48 × (x − 2)

Sum of remaining 7 numbers = 32 × 7 = 224

⇒ 37.81 × (x + 5) = 48 × (x − 2) + 224

⇒ 37.81x + 189.05 = 48x − 96 + 224

⇒ 37.81x + 189.05 = 48x + 128

⇒ 189.05 − 128 = 48x − 37.81x

⇒ 61.05 = 10.19x

⇒ x = 61.05 ÷ 10.19 = 6

⇒ x + 5 = 6 + 5 = 11

⇒ Required sum = 11 × 37.81 = 415.91

∴ Sum of (x + 5) numbers = 415.91

Given:

Number of members in Group A = 81

Number of members in Group B = 29

Number of members in Group C = 70

Average amount spent per member in Group A = ₹467

Average amount spent per member in Group B = ₹117

Average amount spent per member in Group C = ₹378

Formula used:

Total average amount spent per member = (Total amount spent by all groups) ÷ (Total number of members)

Total amount spent by each group = Average amount spent per member × Number of members

Calculation:

Total amount spent by Group A = 467 × 81 = ₹37827

Total amount spent by Group B = 117 × 29 = ₹3393

Total amount spent by Group C = 378 × 70 = ₹26460

Total amount spent by all groups = 37827 + 3393 + 26460 = ₹67680

Total number of members = 81 + 29 + 70 = 180

⇒ Total average amount spent per member = 67680 ÷ 180

⇒ Total average amount spent per member = ₹376

∴ The correct answer is option (4).

Given:

First 15 multiples of 9

Formula used:

Average =

Sum of multiples of a number = n x number x (n + 1) / 2

Calculations:

Multiples of 9: 9, 18, 27, ..., up to 15 terms

Sum = 9 x (1 + 2 + 3 + ... + 15)

⇒ Sum = 9 x

⇒ Sum = 9 x

⇒ Sum = 9 x 120 = 1080

Average =

⇒ Average =

⇒ Average = 72

∴ The correct answer is option (1).

Given:

Average attendance on Sundays = 410

Average attendance on remaining days = 230

Total days in the month = 30

Month starts with Sunday

Concept:

To find the average attendance per day over the month, we need to calculate the total attendance for the month and then divide it by the number of days in the month.

Formula Used:

Total attendance for the month = (Number of Sundays × Average attendance on Sundays) + (Number of other days × Average attendance on other days)

Average attendance per day = Total attendance for the month / Total number of days in the month

Calculation:

We have,

⇒ Number of Sundays in 30 days = 5

⇒ Number of other days in 30 days = 30 - 5 = 25

Using the formula,

⇒ Total attendance for the month = (5 × 410) + (25 × 230)

⇒ Total attendance for the month = 2050 + 5750

⇒ Total attendance for the month = 7800

Now,

⇒ Average attendance per day = 7800 / 30

⇒ Average attendance per day = 260

∴ The average attendance per day of a month of 30 days beginning with Sunday is 260.

Given:

The average marks obtained by all 30 boys of the class is 5 less than the average marks obtained by all 20 girls of the class.

The average marks of the whole class are 25.

Formula Used:

Average marks = Total marks / Total students

Calculation:

Let the average marks of girls be x.

Then, the average marks of boys = x - 5.

Total marks of boys = 30(x - 5)

Total marks of girls = 20x

Total students = 30 + 20 = 50

Given that the average marks of the whole class are 25, we can write:

Total marks of the whole class = 25 × 50 = 1250

Total marks of the whole class = Total marks of boys + Total marks of girls

⇒ 1250 = 30(x - 5) + 20x

⇒ 1250 = 30x - 150 + 20x

⇒ 1250 = 50x - 150

⇒ 1400 = 50x

⇒ x = 1400 / 50

⇒ x = 28

Average marks of girls = x = 28

Average marks of boys = x - 5 = 28 - 5 = 23

Ratio of average marks of boys to that of girls = 23 : 28

The correct answer is option 4.

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