Average MCQ Quiz - Objective Question with Answer for Average - Download Free PDF
Last updated on Apr 19, 2025
Latest Average MCQ Objective Questions
Average Question 1:
Average of numbers A, B & C is 60. If the ratio of sum of A & B to that of C is 7 : 2, then find the value of B. Given that value of A is 20 more than B.
Answer (Detailed Solution Below)
Average Question 1 Detailed Solution
Given:
Average of A, B, and C = 60
The ratio of the sum of A and B to C is 7:2.
A is 20 more than B.
Calculation:
Average of A, B, and C = (A + B + C) / 3 = 60
A + B + C = 60 × 3 = 180
Also, we are given that (A + B) / C = 7 / 2. Therefore:
A + B = (7 / 2) × C
From A = B + 20, substitute this into the equation A + B = (7 / 2) × C:
(B + 20 + B) = (7 / 2) × C
2B + 20 = (7 / 2) × C
Now, we also know that A + B + C = 180. Substitute A = B + 20 into this equation:
(B + 20) + B + C = 180
2B + 20 + C = 180
C = 180 - 2B - 20
C = 160 - 2B
Now substitute C = 160 - 2B into the equation 2B + 20 = (7 / 2) × C:
2B + 20 = (7 / 2) × (160 - 2B)
2B + 20 = 560 - 7B
2B + 7B = 560 - 20
9B = 540
B = 540 / 9 = 60
∴ The value of B is 60.
Average Question 2:
There are 89 members in group A, 59 members in group B and 75 members in group C. All the members of these groups went to a restaurant. The average amount spent on each member of group A, B and C
Answer (Detailed Solution Below)
Average Question 2 Detailed Solution
Given:
Group A: 89 members, Average amount = ₹385
Group B: 59 members, Average amount = ₹277
Group C: 75 members, Average amount = ₹131
Formula used:
Total average = (Total amount spent by all groups) / (Total members)
Calculation:
Total amount by A = 89 × 385 = ₹34265
Total amount by B = 59 × 277 = ₹16343
Total amount by C = 75 × 131 = ₹9825
Total amount spent = 34265 + 16343 + 9825 = ₹60433
Total members = 89 + 59 + 75 = 223
Total average amount = 60433 / 223 ≈ ₹271
∴ Total average amount spent per member = ₹271
Average Question 3:
There are 71 members in group A, 18 members in group B and 53 members in group C. All the members of these groups went to a restaurant. The average amount spent on each member of group A, B and C
Answer (Detailed Solution Below)
Average Question 3 Detailed Solution
Given:
Members in A = 71, B = 18, C = 53
Average spent per member: A = ₹397, B = ₹421, C = ₹137
Formula used:
Total average = (Total amount spent by all) / (Total members)
Calculation:
⇒ Total amount by A = 71 × 397 = 28287
⇒ Total amount by B = 18 × 421 = 7578
⇒ Total amount by C = 53 × 137 = 7261
⇒ Total amount = 28287 + 7578 + 7261 = 43126
⇒ Total members = 71 + 18 + 53 = 142
⇒ Average = 43126 / 142 = 303.0
∴ Total average amount spent per member = ₹303.0
Average Question 4:
The sum of five numbers is 655. The average of the first two numbers is 77 and the third number is 123. Find the average of the remaining two numbers?
Answer (Detailed Solution Below)
Average Question 4 Detailed Solution
Given:
The sum of five numbers is 655.
The average of the first two numbers is 77.
The third number is 123.
Formula Used:
Sum of numbers = Average × Number of terms
Average = Sum of numbers / Number of terms
Calculation:
Sum of the first two numbers = 77 × 2
Sum of the first two numbers = 154
Sum of the first three numbers = 154 + 123
Sum of the first three numbers = 277
Sum of the remaining two numbers = 655 - 277
Sum of the remaining two numbers = 378
Average of the remaining two numbers = 378 / 2
⇒ Average of the remaining two numbers = 189
The average of the remaining two numbers is 189.
Average Question 5:
Nirmal bought 52 books for Rs 1130 from one shop and 47 books for Rs 900 from another. What is the average price (in Rs) he paid per book ?
Answer (Detailed Solution Below)
Average Question 5 Detailed Solution
Given:
Nirmal bought 52 books for Rs 1130 and 47 books for Rs 900.
Formula used:
Average Price per Book = Total Cost / Total Number of Books
Calculation:
Total Cost = 1130 × 52 + 900 × 47
⇒ Total Cost = 58,760 + 42,300 = 101,060
Total Number of Books = 52 + 47
⇒ Total Number of Books = 99
Average Price per Book = 101,060 / 99
⇒ Average Price per Book = 1020.81
∴ The correct answer is option (4).
Top Average MCQ Objective Questions
The average weight of P and his three friends is 55 kg. If P is 4 kg more than the average weight of his three friends, what is P's weight (in kg)?
Answer (Detailed Solution Below)
Average Question 6 Detailed Solution
Download Solution PDFGiven:
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
20 students of a college went to a hotel. 19 of them spent Rs. 175 each on their meal and the 20th student spent Rs. 19 more than the average of all the 20. Find the total money spent by them.
Answer (Detailed Solution Below)
Average Question 7 Detailed Solution
Download Solution PDFGiven:
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
The average age of three persons P, Q and R is 24 years. S joins the group the average age becomes 30 years. If another person T who is 4 years older than S joins the group, then the average age of five persons is ____ years and the age of S is ____ years.
Answer (Detailed Solution Below)
Average Question 8 Detailed Solution
Download Solution PDFLet 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 yearsThe average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
Answer (Detailed Solution Below)
Average Question 9 Detailed Solution
Download Solution PDFGiven:
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
The batting average for 27 innings of a cricket player is 47 runs. His highest score in an innings exceeds his lowest score by 157 runs. If these two innings are excluded, the average score of the remaining 25 innings is 42 runs. Find his highest score in an innings.
Answer (Detailed Solution Below)
Average Question 10 Detailed Solution
Download Solution PDFGiven:
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
The average of nine numbers is 60, that of the first five numbers is 55 and the next three is 65. The ninth number is 10 less than the tenth number. Then, tenth number is –
Answer (Detailed Solution Below)
Average Question 11 Detailed Solution
Download Solution PDFGiven:
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.
The average salary of the entire staff in Reliance Company is Rs.15000 per month. The average salary of officers is Rs.45000 per month and that of non-officers is Rs.10000 per month. If the number of officers is 20 then find the number of non-officers in the Reliance company.
Answer (Detailed Solution Below)
Average Question 12 Detailed Solution
Download Solution PDFGiven:
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
∴ Non-officers in reliance company be 120.Average of 40 numbers is 71. If the number 100 replaced by 140, then average is increased by.
Answer (Detailed Solution Below)
Average Question 13 Detailed Solution
Download Solution PDFGiven:
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
The average weight of 20 students in a group is 54 kg. If 12 students of average weight 52 kg join the group and 7 students of average weight 56 kg leave the group, then what will be the average weight (in kg) of the remaining students in the group?
Answer (Detailed Solution Below)
Average Question 14 Detailed Solution
Download Solution PDFGiven:-
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.
The average of 45 numbers is 150. Later it is found that a number 46 is wrongly written as 91, then find the correct average.
Answer (Detailed Solution Below)
Average Question 15 Detailed Solution
Download Solution PDFGiven:
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